Automorphisms Of Manifolds And Algebraic K Theory Part Iii

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Automorphisms of Manifolds and Algebraic $K$-Theory: Part III

Author : Michael S. Weiss
Publisher : American Mathematical Soc.
ISBN 13 : 147040981X
Total Pages : 122 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Automorphisms of Manifolds and Algebraic $K$-Theory: Part III by : Michael S. Weiss

Download or read book Automorphisms of Manifolds and Algebraic $K$-Theory: Part III written by Michael S. Weiss and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.

Surveys on Surgery Theory

Author : Sylvain E. Cappell
Publisher : Princeton University Press
ISBN 13 : 9780691049380
Total Pages : 452 pages
Book Rating : 4.0/5 (493 download)

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Book Synopsis Surveys on Surgery Theory by : Sylvain E. Cappell

Download or read book Surveys on Surgery Theory written by Sylvain E. Cappell and published by Princeton University Press. This book was released on 2000-01-10 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

A Homology Theory for Smale Spaces

Author : Ian F. Putnam
Publisher : American Mathematical Soc.
ISBN 13 : 1470409097
Total Pages : 136 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Homology Theory for Smale Spaces by : Ian F. Putnam

Download or read book A Homology Theory for Smale Spaces written by Ian F. Putnam and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

Irreducible Almost Simple Subgroups of Classical Algebraic Groups

Author : Timothy C. Burness
Publisher : American Mathematical Soc.
ISBN 13 : 147041046X
Total Pages : 122 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Irreducible Almost Simple Subgroups of Classical Algebraic Groups by : Timothy C. Burness

Download or read book Irreducible Almost Simple Subgroups of Classical Algebraic Groups written by Timothy C. Burness and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Author : Gaëtan Chenevier
Publisher : American Mathematical Soc.
ISBN 13 : 147041094X
Total Pages : 134 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Level One Algebraic Cusp Forms of Classical Groups of Small Rank by : Gaëtan Chenevier

Download or read book Level One Algebraic Cusp Forms of Classical Groups of Small Rank written by Gaëtan Chenevier and published by American Mathematical Soc.. This book was released on 2015-08-21 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.

A Geometric Theory for Hypergraph Matching

Author : Peter Keevash
Publisher : American Mathematical Soc.
ISBN 13 : 1470409658
Total Pages : 108 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Geometric Theory for Hypergraph Matching by : Peter Keevash

Download or read book A Geometric Theory for Hypergraph Matching written by Peter Keevash and published by American Mathematical Soc.. This book was released on 2014-12-20 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: `space barriers' from convex geometry, and `divisibility barriers' from arithmetic lattice-based constructions. To formulate precise results, they introduce the setting of simplicial complexes with minimum degree sequences, which is a generalisation of the usual minimum degree condition. They determine the essentially best possible minimum degree sequence for finding an almost perfect matching. Furthermore, their main result establishes the stability property: under the same degree assumption, if there is no perfect matching then there must be a space or divisibility barrier. This allows the use of the stability method in proving exact results. Besides recovering previous results, the authors apply our theory to the solution of two open problems on hypergraph packings: the minimum degree threshold for packing tetrahedra in -graphs, and Fischer's conjecture on a multipartite form of the Hajnal-Szemerédi Theorem. Here they prove the exact result for tetrahedra and the asymptotic result for Fischer's conjecture; since the exact result for the latter is technical they defer it to a subsequent paper.

Local Entropy Theory of a Random Dynamical System

Author : Anthony H. Dooley
Publisher : American Mathematical Soc.
ISBN 13 : 1470410559
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Local Entropy Theory of a Random Dynamical System by : Anthony H. Dooley

Download or read book Local Entropy Theory of a Random Dynamical System written by Anthony H. Dooley and published by American Mathematical Soc.. This book was released on 2014-12-20 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

The Optimal Version of Hua's Fundamental Theorem of Geometry of Rectangular Matrices

Author : Peter Šemrl
Publisher : American Mathematical Soc.
ISBN 13 : 0821898450
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Optimal Version of Hua's Fundamental Theorem of Geometry of Rectangular Matrices by : Peter Šemrl

Download or read book The Optimal Version of Hua's Fundamental Theorem of Geometry of Rectangular Matrices written by Peter Šemrl and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m\times n matrices over a division ring \mathbb{D} which preserve adjacency in both directions. Motivated by several applications the author studies a long standing open problem of possible improvements. There are three natural questions. Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only and still get the same conclusion? Can we relax the bijectivity assumption? Can we obtain an analogous result for maps acting between the spaces of rectangular matrices of different sizes? A division ring is said to be EAS if it is not isomorphic to any proper subring. For matrices over EAS division rings the author solves all three problems simultaneously, thus obtaining the optimal version of Hua's theorem. In the case of general division rings he gets such an optimal result only for square matrices and gives examples showing that it cannot be extended to the non-square case.

Polynomial Approximation on Polytopes

Author : Vilmos Totik
Publisher : American Mathematical Soc.
ISBN 13 : 1470416662
Total Pages : 124 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Polynomial Approximation on Polytopes by : Vilmos Totik

Download or read book Polynomial Approximation on Polytopes written by Vilmos Totik and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial approximation on convex polytopes in is considered in uniform and -norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the -case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate -functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

The Grothendieck Inequality Revisited

Author : Ron Blei
Publisher : American Mathematical Soc.
ISBN 13 : 0821898558
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Grothendieck Inequality Revisited by : Ron Blei

Download or read book The Grothendieck Inequality Revisited written by Ron Blei and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved, concerning continuous functions of two variables over general topological domains. The main result is the construction of a continuous map $\Phi$ from $l^2(A)$ into $L^2(\Omega_A, \mathbb{P}_A)$, where $A$ is a set, $\Omega_A = \{-1,1\}^A$, and $\mathbb{P}_A$ is the uniform probability measure on $\Omega_A$.

Transfer of Siegel Cusp Forms of Degree 2

Author : Ameya Pitale
Publisher : American Mathematical Soc.
ISBN 13 : 0821898566
Total Pages : 120 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Transfer of Siegel Cusp Forms of Degree 2 by : Ameya Pitale

Download or read book Transfer of Siegel Cusp Forms of Degree 2 written by Ameya Pitale and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and

Imprimitive Irreducible Modules for Finite Quasisimple Groups

Author : Gerhard Hiss
Publisher : American Mathematical Soc.
ISBN 13 : 1470409607
Total Pages : 126 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Imprimitive Irreducible Modules for Finite Quasisimple Groups by : Gerhard Hiss

Download or read book Imprimitive Irreducible Modules for Finite Quasisimple Groups written by Gerhard Hiss and published by American Mathematical Soc.. This book was released on 2015-02-06 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the maximal subgroup problem of the finite classical groups the authors begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields K. A module of a group G over K is imprimitive, if it is induced from a module of a proper subgroup of G. The authors obtain their strongest results when char(K)=0, although much of their analysis carries over into positive characteristic. If G is a finite quasisimple group of Lie type, they prove that an imprimitive irreducible KG-module is Harish-Chandra induced. This being true for \rm char(K) different from the defining characteristic of G, the authors specialize to the case char(K)=0 and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. The authors determine the asymptotic proportion of the irreducible imprimitive KG-modules, when G runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of their investigations is the fact that these proportions tend to 1, if the Lie rank of the groups tends to infinity. For exceptional groups G of Lie type of small rank, and for sporadic groups G, the authors determine all irreducible imprimitive KG-modules for arbitrary characteristic of K.

Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model

Author : Raphaël Cerf
Publisher : American Mathematical Soc.
ISBN 13 : 1470409674
Total Pages : 100 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model by : Raphaël Cerf

Download or read book Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model written by Raphaël Cerf and published by American Mathematical Soc.. This book was released on 2014-12-20 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size of chromosomes of length over an alphabet of cardinality . The mutation probability per locus is . He deals only with the sharp peak landscape: the replication rate is for the master sequence and for the other sequences. He studies the equilibrium distribution of the process in the regime where

Shock Waves in Conservation Laws with Physical Viscosity

Author : Tai-Ping Liu
Publisher : American Mathematical Soc.
ISBN 13 : 1470410168
Total Pages : 180 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Shock Waves in Conservation Laws with Physical Viscosity by : Tai-Ping Liu

Download or read book Shock Waves in Conservation Laws with Physical Viscosity written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 2015-02-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the perturbation of a shock wave in conservation laws with physical viscosity. They obtain the detailed pointwise estimates of the solutions. In particular, they show that the solution converges to a translated shock profile. The strength of the perturbation and that of the shock are assumed to be small but independent. The authors' assumptions on the viscosity matrix are general so that their results apply to the Navier-Stokes equations for the compressible fluid and the full system of magnetohydrodynamics, including the cases of multiple eigenvalues in the transversal fields, as long as the shock is classical. The authors' analysis depends on accurate construction of an approximate Green's function. The form of the ansatz for the perturbation is carefully constructed and is sufficiently tight so that the author can close the nonlinear term through Duhamel's principle.

Julia Sets and Complex Singularities of Free Energies

Author : Jianyong Qiao
Publisher : American Mathematical Soc.
ISBN 13 : 1470409828
Total Pages : 102 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Julia Sets and Complex Singularities of Free Energies by : Jianyong Qiao

Download or read book Julia Sets and Complex Singularities of Free Energies written by Jianyong Qiao and published by American Mathematical Soc.. This book was released on 2015-02-06 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies a family of renormalization transformations of generalized diamond hierarchical Potts models through complex dynamical systems. He proves that the Julia set (unstable set) of a renormalization transformation, when it is treated as a complex dynamical system, is the set of complex singularities of the free energy in statistical mechanics. He gives a sufficient and necessary condition for the Julia sets to be disconnected. Furthermore, he proves that all Fatou components (components of the stable sets) of this family of renormalization transformations are Jordan domains with at most one exception which is completely invariant. In view of the problem in physics about the distribution of these complex singularities, the author proves here a new type of distribution: the set of these complex singularities in the real temperature domain could contain an interval. Finally, the author studies the boundary behavior of the first derivative and second derivative of the free energy on the Fatou component containing the infinity. He also gives an explicit value of the second order critical exponent of the free energy for almost every boundary point.

Analysis of the Hodge Laplacian on the Heisenberg Group

Author : Detlef Muller
Publisher : American Mathematical Soc.
ISBN 13 : 1470409399
Total Pages : 104 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Analysis of the Hodge Laplacian on the Heisenberg Group by : Detlef Muller

Download or read book Analysis of the Hodge Laplacian on the Heisenberg Group written by Detlef Muller and published by American Mathematical Soc.. This book was released on 2014-12-20 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1

Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture

Author : Joel Friedman
Publisher : American Mathematical Soc.
ISBN 13 : 1470409887
Total Pages : 124 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture by : Joel Friedman

Download or read book Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture written by Joel Friedman and published by American Mathematical Soc.. This book was released on 2014-12-20 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.