Homological Group Theory

Homological Group Theory

Author: Charles Terence Clegg Wall

Publisher: Cambridge University Press

Published: 1979-12-27

Total Pages: 409

ISBN-13: 0521227291

DOWNLOAD EBOOK

Eminent mathematicians have presented papers on homological and combinatorial techniques in group theory. The lectures are aimed at presenting in a unified way new developments in the area.


Topological Methods in Group Theory

Topological Methods in Group Theory

Author: Ross Geoghegan

Publisher: Springer Science & Business Media

Published: 2007-12-17

Total Pages: 473

ISBN-13: 0387746110

DOWNLOAD EBOOK

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.


Homology Theory

Homology Theory

Author: James W. Vick

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 258

ISBN-13: 1461208815

DOWNLOAD EBOOK

This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.


Cohomology of Groups

Cohomology of Groups

Author: Kenneth S. Brown

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 318

ISBN-13: 1468493272

DOWNLOAD EBOOK

Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.


An Introduction to Homological Algebra

An Introduction to Homological Algebra

Author: Northcott

Publisher: Cambridge University Press

Published: 1960

Total Pages: 294

ISBN-13: 9780521058414

DOWNLOAD EBOOK

Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott's aim is to introduce homological ideas and methods and to show some of the results which can be achieved. The early chapters provide the results needed to establish the theory of derived functors and to introduce torsion and extension functors. The new concepts are then applied to the theory of global dimensions, in an elucidation of the structure of commutative Noetherian rings of finite global dimension and in an account of the homology and cohomology theories of monoids and groups. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. This book is designed with the needs and problems of the beginner in mind, providing a helpful and lucid account for those about to begin research, but will also be a useful work of reference for specialists. It can also be used as a textbook for an advanced course.


An Introduction to Homological Algebra

An Introduction to Homological Algebra

Author: Charles A. Weibel

Publisher: Cambridge University Press

Published: 1995-10-27

Total Pages: 470

ISBN-13: 113964307X

DOWNLOAD EBOOK

The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.


Elements of Homology Theory

Elements of Homology Theory

Author: Viktor Vasilʹevich Prasolov

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 432

ISBN-13: 0821838121

DOWNLOAD EBOOK

The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.


Homological Algebra (PMS-19), Volume 19

Homological Algebra (PMS-19), Volume 19

Author: Henry Cartan

Publisher: Princeton University Press

Published: 2016-06-02

Total Pages: 408

ISBN-13: 1400883849

DOWNLOAD EBOOK

When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.


A Basic Course in Algebraic Topology

A Basic Course in Algebraic Topology

Author: William S. Massey

Publisher: Springer

Published: 2019-06-28

Total Pages: 448

ISBN-13: 1493990632

DOWNLOAD EBOOK

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.