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Tilings Of The Plane Hyperbolic Groups And Small Cancellation Conditions
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Book Synopsis Tilings of the Plane, Hyperbolic Groups, and Small Cancellation Conditions by : Milé Krajčevski
Download or read book Tilings of the Plane, Hyperbolic Groups, and Small Cancellation Conditions written by Milé Krajčevski and published by . This book was released on 2014-09-11 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface Acknowledgments Introduction Small cancellation theory of $\mathcal{T}$ Tilings Bibliography.
Book Synopsis Tilings of the Plane, Hyperbolic Groups and Small Cancellation Conditions by : Milé Krajčevski
Download or read book Tilings of the Plane, Hyperbolic Groups and Small Cancellation Conditions written by Milé Krajčevski and published by American Mathematical Soc.. This book was released on 2001 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
Book Synopsis Homotopy Theory of the Suspensions of the Projective Plane by : Jie Wu
Download or read book Homotopy Theory of the Suspensions of the Projective Plane written by Jie Wu and published by American Mathematical Soc.. This book was released on 2003 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The homotopy theory of the suspensions of the real projective plane is largely investigated. The homotopy groups are computed up to certain range. The decompositions of the self smashes and the loop spaces are studied with some applications to the Stiefel manifolds.
Book Synopsis Topological Invariants of the Complement to Arrangements of Rational Plane Curves by : José Ignacio Cogolludo-Agustín
Download or read book Topological Invariants of the Complement to Arrangements of Rational Plane Curves written by José Ignacio Cogolludo-Agustín and published by American Mathematical Soc.. This book was released on 2002 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors analyse two topological invariants of an embedding of an arrangement of rational plane curves in the projective complex plane, namely, the cohomology ring of the complement and the characteristic varieties. Their main result states that the cohomology ring of the complement to a rational arrangement is generated by logarithmic 1 and 2-forms and its structure depends on a finite number of invariants of the curve (its combinatorial type).
Book Synopsis Connectivity Properties of Group Actions on Non-Positively Curved Spaces by : Robert Bieri
Download or read book Connectivity Properties of Group Actions on Non-Positively Curved Spaces written by Robert Bieri and published by American Mathematical Soc.. This book was released on 2003 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ to group actions $\rho$ implies the introduction of 'Sigma invariants' $\Sigma^k(\rho)$ to replace the previous $\Sigma^k(G)$ introduced by those authors. Their theory is now seen as a special case of what is studied here so that readers seeking a detailed treatment of their theory will find it included here as a special case. We define and study 'controlled $k$-connectedness $(CC^k)$' of $\rho$, both over $M$ and over end points $e$ in the 'boundary at infinity' $\partial M$; $\Sigma^k(\rho)$ is by definition the set of all $e$ over which the action is $(k-1)$-connected. A central theorem, the Boundary Criterion, says that $\Sigma^k(\rho) = \partial M$ if and only if $\rho$ is $CC^{k-1}$ over $M$.An Openness Theorem says that $CC^k$ over $M$ is an open condition on the space of isometric actions $\rho$ of $G$ on $M$. Another Openness Theorem says that $\Sigma^k(\rho)$ is an open subset of $\partial M$ with respect to the Tits metric topology. When $\rho(G)$ is a discrete group of isometries the property $CC^{k-1}$ is equivalent to ker$(\rho)$ having the topological finiteness property type '$F_k$'. More generally, if the orbits of the action are discrete, $CC^{k-1}$ is equivalent to the point-stabilizers having type $F_k$. In particular, for $k=2$ we are characterizing finite presentability of kernels and stabilizers. Examples discussed include: locally rigid actions, translation actions on vector spaces (especially those by metabelian groups), actions on trees (including those of $S$-arithmetic groups on Bruhat-Tits trees), and $SL_2$ actions on the hyperbolic plane.
Book Synopsis From Representation Theory to Homotopy Groups by : Donald M. Davis
Download or read book From Representation Theory to Homotopy Groups written by Donald M. Davis and published by American Mathematical Soc.. This book was released on 2002 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: A formula for the odd-primary v1-periodic homotopy groups of a finite H-space in terms of its K-theory and Adams operations has been obtained by Bousfield. This work applies this theorem to give explicit determinations of the v1-periodic homotopy groups of (E8,5) and (E8,3), thus completing the determination of all odd-primary v1-periodic homotopy groups of all compact simple Lie groups, a project suggested by Mimura in 1989. The method is different to that used by the author in previous works. There is no homotopy theoretic input, and no spectral sequence calculation. The input is the second exterior power operation in the representation ring of E8, which we determine using specialized software. This can be interpreted as giving the Adams operation psi^2 in K(E8). Eigenvectors of psi^2 must also be eigenvectors of psi^k for any k. The matrix of these eigenvectors is the key to the analysis. Its determinant is closely related to the homotopy decomposition of E8 localized at each prime. By taking careful combinations of eigenvectors, a set of generators of K(E8) can be obtained on which there is a nice formula for all Adams operations. Bousfield's theorem (and considerable Maple computation) allows the v1-periodic homotopy groups to be obtained from this.
Book Synopsis Almost Commuting Elements in Compact Lie Groups by : Armand Borel
Download or read book Almost Commuting Elements in Compact Lie Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2002 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in the extended Dynkin diagram of the simply connected cover, together with the co-root integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
Book Synopsis The Connective K-Theory of Finite Groups by : Robert Ray Bruner
Download or read book The Connective K-Theory of Finite Groups written by Robert Ray Bruner and published by American Mathematical Soc.. This book was released on 2003 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group
Book Synopsis The Based Ring of Two-Sided Cells of Affine Weyl Groups of Type $\widetilde {A}_{n-1}$ by : Nanhua Xi
Download or read book The Based Ring of Two-Sided Cells of Affine Weyl Groups of Type $\widetilde {A}_{n-1}$ written by Nanhua Xi and published by American Mathematical Soc.. This book was released on 2002 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type $\tilde A_{n-1}$.
Book Synopsis Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation by : L. Rodman
Download or read book Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation written by L. Rodman and published by American Mathematical Soc.. This book was released on 2002 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: New versions are developed of an abstract scheme, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results allow us to prove, among other things, that the band extension is continuous in an appropriate sense. Using the new versions of the abstract band method, we solve the positive extension problem for almost periodic matrix functions of several real variables with Fourier coefficients indexed in a given additive subgroup of the space of variables.This generality allows us to treat simultaneously many particular cases, for example the case of functions periodic in some variables and almost periodic in others. Necessary and sufficient conditions are given for the existence of positive extensions in terms of Toeplitz operators on Besikovitch spaces. Furthermore, when a solution exists a special extension (the band extension) is constructed which enjoys a maximum entropy property.A linear fractional parameterization of the set of all extensions is also provided. We interpret the obtained results (in the periodic case) in terms of existence of a multivariate autoregressive moving averages (ARMA) process with given autocorrelation coefficients, and identify its maximal prediction error. Another application concerns the solution of the positive extension problem in the context of Wiener algebra of infinite operator matrices. It includes the identification of the maximum entropy extension and a description of all positive extensions via a linear fractional formula. In the periodic case it solves a linear estimation problem for cyclostationary stochastic processes.
Book Synopsis Homotopy Theory of Diagrams by : Wojciech Chachólski
Download or read book Homotopy Theory of Diagrams written by Wojciech Chachólski and published by American Mathematical Soc.. This book was released on 2002 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors develop homotopy theoretical methods for studying diagrams. In particular they explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept introduced is that of a model approximation. A model approximation of a category $\mathcal{C}$ with a given class of weak equivalences is a model category $\mathcal{M}$ together with a pair of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which satisfy certain properties. The key result says that if $\mathcal{C}$ admits a model approximation then so does the functor category $Fun(I, \mathcal{C})$.
Book Synopsis The Submanifold Geometries Associated to Grassmannian Systems by : Martina Brück
Download or read book The Submanifold Geometries Associated to Grassmannian Systems written by Martina Brück and published by American Mathematical Soc.. This book was released on 2002 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
Book Synopsis Blowing Up of Non-Commutative Smooth Surfaces by : M. van den Bergh
Download or read book Blowing Up of Non-Commutative Smooth Surfaces written by M. van den Bergh and published by American Mathematical Soc.. This book was released on 2001 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text looks at topics that include: preliminaries on category theory; non-commutative geometry; pseudo-compact rings; Cohen-Macaulay curves embedded in quasi-schemes; derived categories; quantum plane geometry; and non-commutative cubic surfaces.
Book Synopsis Mutual Invadability Implies Coexistence in Spatial Models by : Richard Durrett
Download or read book Mutual Invadability Implies Coexistence in Spatial Models written by Richard Durrett and published by American Mathematical Soc.. This book was released on 2002 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.
Book Synopsis Segre's Reflexivity and an Inductive Characterization of Hyperquadrics by : Yasuyuki Kachi
Download or read book Segre's Reflexivity and an Inductive Characterization of Hyperquadrics written by Yasuyuki Kachi and published by American Mathematical Soc.. This book was released on 2002 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction The universal pseudo-quotient for a family of subvarieties Normal bundles of quadrics in $X$ Morphisms from quadrics to Grassmannians Pointwise uniform vector bundles on non-singular quadrics Theory of extensions of families over Hilbert schemes Existence of algebraic quotient--proof of Theorem 0.3 Appendix. Deformations of vector bundles on infinitesimally rigid projective varieties with null global $i$-forms References
Book Synopsis Triangulations of Oriented Matroids by : Francisco Santos
Download or read book Triangulations of Oriented Matroids written by Francisco Santos and published by American Mathematical Soc.. This book was released on 2002 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.
Book Synopsis A Stability Index Analysis of 1-D Patterns of the Gray-Scott Model by : A. Doelman
Download or read book A Stability Index Analysis of 1-D Patterns of the Gray-Scott Model written by A. Doelman and published by American Mathematical Soc.. This book was released on 2002 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is intended for graduate students and research mathematicians interested in partial differential equations.
