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Iterating The Cobar Construction
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Book Synopsis Iterating the Cobar Construction by : Justin R. Smith
Download or read book Iterating the Cobar Construction written by Justin R. Smith and published by American Mathematical Soc.. This book was released on 1994 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a new invariant of a CW-complex called the m-structure and uses it to perform homotopy-theoretic computations. The m-structure of a space encapsulates the coproduct structure, as well as higher-coproduct structures that determine Steenrod-operations. Given an m-structure on the chain complex of a reduced simplicial complex of a pointed simply-connected space, one can equip the cobar construction of this chain-complex with a natural m-structure. This result allows one to form iterated cobar constructions that are shown to be homotopy equivalent to iterated loop-spaces.
Book Synopsis Geometry of Loop Spaces and the Cobar Construction by : Hans J. Baues
Download or read book Geometry of Loop Spaces and the Cobar Construction written by Hans J. Baues and published by American Mathematical Soc.. This book was released on 1980 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The homology of iterated loop spaces [capital Greek]Omega [superscript]n [italic]X has always been a problem of major interest because it gives some insight into the homotopy of [italic]X, among other things. Therefore, if [italic]X is a CW-complex, one has been interested in small CW models for [capital Greek]Omega [superscript]n [italic]X in order to compute the cellular chain complex. The author proves a very general model theorem from which he can derive models, in addition to very technical proofs of the model theorem for several other models.
Book Synopsis Hilbert's Projective Metric and Iterated Nonlinear Maps by : Roger D. Nussbaum
Download or read book Hilbert's Projective Metric and Iterated Nonlinear Maps written by Roger D. Nussbaum and published by American Mathematical Soc.. This book was released on 1988 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book H - Spaces written by Francois Sigrist and published by Springer. This book was released on 2006-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operads in Algebra, Topology and Physics by : Martin Markl
Download or read book Operads in Algebra, Topology and Physics written by Martin Markl and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.
Book Synopsis A User's Guide to Spectral Sequences by : John McCleary
Download or read book A User's Guide to Spectral Sequences written by John McCleary and published by Cambridge University Press. This book was released on 2001 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
Book Synopsis Handbook of Algebraic Topology by : I.M. James
Download or read book Handbook of Algebraic Topology written by I.M. James and published by Elsevier. This book was released on 1995-07-18 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.
Book Synopsis Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ by : Mauro Beltrametti
Download or read book Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ written by Mauro Beltrametti and published by American Mathematical Soc.. This book was released on 1995 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.
Book Synopsis Textile Systems for Endomorphisms and Automorphisms of the Shift by : Masakazu Nasu
Download or read book Textile Systems for Endomorphisms and Automorphisms of the Shift written by Masakazu Nasu and published by American Mathematical Soc.. This book was released on 1995 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.
Book Synopsis On Finite Groups and Homotopy Theory by : Ran Levi
Download or read book On Finite Groups and Homotopy Theory written by Ran Levi and published by American Mathematical Soc.. This book was released on 1995 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: In part 1 we study the homology, homotopy, and stable homotopy of [capital Greek]Omega[italic capital]B[lowercase Greek]Pi[up arrowhead][over][subscript italic]p, where [italic capital]G is a finite [italic]p-perfect group. In part 2 we define the concept of resolutions by fibrations over an arbitrary family of spaces.
Book Synopsis The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations by : Shirō Gotō
Download or read book The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations written by Shirō Gotō and published by American Mathematical Soc.. This book was released on 1994 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first, this volume was intended to be an investigation of symbolic blow-up rings for prime ideals defining curve singularities. The motivation for that has come from the recent 3-dimensional counterexamples to Cowsik's question, given by the authors and Watanabe: it has to be helpful, for further researches on Cowsik's question and a related problem of Kronecker, to generalize their methods to those of a higher dimension. However, while the study was progressing, it proved apparent that the framework of Part I still works, not only for the rather special symbolic blow-up rings but also in the study of Rees algebras R(F) associated to general filtrations F = {F[subscript]n} [subscript]n [subscript][set membership symbol][subscript bold]Z of ideals. This observation is closely explained in Part II of this volume, as a general ring-theory of Rees algebras R(F). We are glad if this volume will be a new starting point for the further researchers on Rees algebras R(F) and their associated graded rings G(F).
Book Synopsis Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$ by : A. L. Levin
Download or read book Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$ written by A. L. Levin and published by American Mathematical Soc.. This book was released on 1994 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bounds for orthogonal polynomials which hold on the 'whole' interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on [-1,1]. Also presented are uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.
Book Synopsis Diagram Cohomology and Isovariant Homotopy Theory by : Giora Dula
Download or read book Diagram Cohomology and Isovariant Homotopy Theory written by Giora Dula and published by American Mathematical Soc.. This book was released on 1994 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Obstruction theoretic methods are introduced into isovariant homotopy theory for a class of spaces with group actions; the latter includes all smooth actions of cyclic groups of prime power order. The central technical result is an equivalence between isovariant homotopy and specific equivariant homotopy theories for diagrams under suitable conditions. This leads to isovariant Whitehead theorems, an obstruction-theoretic approach to isovariant homotopy theory with obstructions in cohomology groups of ordinary and equivalent diagrams, and qualitative computations for rational homotopy groups of certain spaces of isovariant self maps of linear spheres. The computations show that these homotopy groups are often far more complicated than the rational homotopy groups for the corresponding spaces of equivariant self maps. Subsequent work will use these computations to construct new families of smooth actions on spheres that are topologically linear but differentiably nonlinear.
Book Synopsis Global Aspects of Homoclinic Bifurcations of Vector Fields by : Ale Jan Homburg
Download or read book Global Aspects of Homoclinic Bifurcations of Vector Fields written by Ale Jan Homburg and published by American Mathematical Soc.. This book was released on 1996 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author investigates a class of smooth one parameter families of vector fields on some $n$-dimensional manifold, exhibiting a homoclinic bifurcation. That is, he considers generic families $x_\mu$, where $x_0$ has a distinguished hyperbolic singularity $p$ and a homoclinic orbit; an orbit converging to $p$ both for positive and negative time. It is assumed that this homoclinic orbit is of saddle-saddle type, characterized by the existence of well-defined directions along which it converges to the singularity $p$. The study is not confined to a small neighborhood of the homoclinic orbit. Instead, the position of the stable and unstable set of the homoclinic orbit is incorporated and it is shown that homoclinic bifurcations can lead to complicated bifurcations and dynamics, including phenomena like intermittency and annihilation of suspended horseshoes.
Book Synopsis Tilting in Abelian Categories and Quasitilted Algebras by : Dieter Happel
Download or read book Tilting in Abelian Categories and Quasitilted Algebras written by Dieter Happel and published by American Mathematical Soc.. This book was released on 1996 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: We generalize tilting with respect to a tilting module of projective dimension at most one for an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting algebras which we call quasitilted algebras. This class also contains the canonical algebras, and we show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. We also give other characterizations of quasitilted algebras, and give methods for constructing such algebras.
Book Synopsis Inverse Nodal Problems: Finding the Potential from Nodal Lines by : Ole H. Hald
Download or read book Inverse Nodal Problems: Finding the Potential from Nodal Lines written by Ole H. Hald and published by American Mathematical Soc.. This book was released on 1996 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.
Book Synopsis Deformation Theory of Pseudogroup Structures by : Victor Guillemin
Download or read book Deformation Theory of Pseudogroup Structures written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 1966 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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