Iterating The Cobar Construction

Author : Justin R. Smith
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 53,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825884

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Iterating the Cobar Construction by Justin R. Smith Pdf

This book develops a new topological invariant called the m-structure, which incorporates all information contained in the canonical coproduct and the Steenrod operations. Given a chain complex equipped with an m-structure, Smith shows that its cobar construction also has a natural m-structure. This derived m-structure of the cobar construction corresponds to the m-structure of the loop space of the original space under the map that carries the cobar construction to the loop space. This result allows one to form iterated cobar constructions which Smith shows are homotopy equivalent to iterated loop spaces. These results are applied to the computation of the cohomology algebra structure of total spaces of fibrations.

Author : Hans J. Baues
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 43,9 Mb
Release : 1980
Category : Mathematics
ISBN : 9780821822302

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Geometry of Loop Spaces and the Cobar Construction by Hans J. Baues Pdf

Author : Roger D. Nussbaum
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 46,7 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821824542

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Hilbert's Projective Metric and Iterated Nonlinear Maps by Roger D. Nussbaum Pdf

Author : Francois Sigrist
Publisher : Springer
Page : 165 pages
File Size : 55,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540366218

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H - Spaces by Francois Sigrist Pdf

Author : Martin Markl,Steven Shnider,James D. Stasheff
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 44,8 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821843628

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Operads in Algebra, Topology and Physics by Martin Markl,Steven Shnider,James D. Stasheff Pdf

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.

Author : John McCleary
Publisher : Cambridge University Press
Page : 579 pages
File Size : 45,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9780521567596

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A User's Guide to Spectral Sequences by John McCleary Pdf

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.

Author : I.M. James
Publisher : Elsevier
Page : 1336 pages
File Size : 48,5 Mb
Release : 1995-07-18
Category : Mathematics
ISBN : 9780080532981

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Handbook of Algebraic Topology by I.M. James Pdf

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.

Author : Mauro Beltrametti,Michael Schneider,Andrew John Sommese
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 43,9 Mb
Release : 1995
Category : Adjunction theory
ISBN : 9780821802342

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Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ by Mauro Beltrametti,Michael Schneider,Andrew John Sommese Pdf

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.

Author : Masakazu Nasu
Publisher : American Mathematical Soc.
Page : 215 pages
File Size : 43,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826065

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Textile Systems for Endomorphisms and Automorphisms of the Shift by Masakazu Nasu Pdf

One of the major topics in symbolic dynamics is the analysis of the dynamical systems defined by endomorphisms and automorphisms of subshifts. This includes analysis of the dynamical behavior of one-dimensional cellular automata as a special case. In this work, Nasu introduces the notion of a textile system, which is useful in analyzing the dynamical systems defined by endomorphisms and automorphisms of topological Markov shifts, including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied. Requiring few prerequisites, this work will appeal not only to specialists in symbolic dynamics but also to nonspecialists interested in symbolic dynamics and those interested in analysis of the dynamical behavior of cellular automata.

Author : Ran Levi
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 47,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804018

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On Finite Groups and Homotopy Theory by Ran Levi Pdf

Let $p$ be a fixed prime number. Let $G$ denote a finite $p$-perfect group. This book looks at the homotopy type of the $p$-completed classifying space $BG_p$, where $G$ is a finite $p$-perfect group. The author constructs an algebraic analog of the Quillen's ``plus'' construction for differential graded coalgebras. This construction is used to show that given a finite $p$-perfect group $G$, the loop spaces $BG_p$ admits integral homology exponents. Levi gives examples to show that in some cases our bound is best possible. It is shown that in general $B\ast _p$ admits infinitely many non-trivial $k$-invariants. The author presents examples where homotopy exponents exist. Classical constructions in stable homotopy theory are used to show that the stable homotopy groups of these loop spaces also have exponents.

Author : Shirō Gotō,Koji Nishida
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 42,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825846

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The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations by Shirō Gotō,Koji Nishida Pdf

This monograph consists of two parts. Part I investigates the Cohen-Macaulay and Gorenstein properties of symbolic Rees algebras for one-dimensional prime ideals in Cohen-Macaulay local rings. Practical criteria for these algebras to be Cohen-Macaulay and Gorenstein rings are described in terms of certain elements in the prime ideals. This framework is generalized in Part II to Rees algebras $R(F)$ and graded rings $G(F)$ associated to general filtrations of ideals in arbitrary Noetherian local rings. Goto and Nishida give certain cohomological characterizations for algebras $R(F)$ to be Cohen-Macaulay or Gorenstein rings in connection with the corresponding ring-theoretic properties of $G(F)$. In this way, readers follow a history of the development of the ring theory of Rees algebras. The book raises many important open questions.

Author : A. L. Levin,Doron Shaul Lubinsky
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 44,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825990

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Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$ by A. L. Levin,Doron Shaul Lubinsky Pdf

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 $[-1,1]$. Levin and Lubinsky obtain such bounds for weights that vanish strongly at 1 and $-1$. They also present uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Author : Giora Dula,Reinhard Schultz
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 46,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825891

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Diagram Cohomology and Isovariant Homotopy Theory by Giora Dula,Reinhard Schultz Pdf

In algebraic topology, obstruction theory provides a way to study homotopy classes of continuous maps in terms of cohomology groups; a similar theory exists for certain spaces with group actions and maps that are compatible (that is, equivariant) with respect to the group actions. This work provides a corresponding setting for certain spaces with group actions and maps that are compatible in a stronger sense, called isovariant. The basic idea is to establish an equivalence between isovariant homotopy and equivariant homotopy for certain categories of diagrams. Consequences include isovariant versions of the usual Whitehead theorems for recognizing homotopy equivalences, an obstruction theory for deforming equivariant maps to isovariant maps, rational computations for the homotopy groups of certain spaces of isovariant functions, and applications to constructions and classification problems for differentiable group actions.

Author : Ale Jan Homburg
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 47,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804414

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Global Aspects of Homoclinic Bifurcations of Vector Fields by Ale Jan Homburg Pdf

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.

Author : Dieter Happel,Idun Reiten,Sverre O. Smalø
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 54,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804445

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Tilting in Abelian Categories and Quasitilted Algebras by Dieter Happel,Idun Reiten,Sverre O. Smalø Pdf

In this book, the authors generalize 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. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call ``quasitilted algebras''. This class also contains the canonical algebras, and the authors 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. The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when one-point extensions of hereditary algebras are quasitilted.