**Author**: Frank Albert Raymond

**Publisher:**

**ISBN:**

**Size**: 67.45 MB

**Format:**PDF, Kindle

**Category :**Homology theory

**Languages :**en

**Pages :**156

**View:**4596

**Book Description:**

## On The Uniqueness Theorem Of Local Homology Theory

**Author**: Sze-Tsen Hu

**Publisher:**

**ISBN:**

**Size**: 51.39 MB

**Format:**PDF, ePub, Docs

**Category :**Homology theory

**Languages :**en

**Pages :**13

**View:**7642

**Book Description:**

## Stable Homotopy And Generalised Homology

**Author**: J. F. Adams

**Publisher:**University of Chicago Press

**ISBN:**9780226005249

**Size**: 49.53 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**373

**View:**5859

**Book Description:**J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.

## Homology

**Author**: Saunders Mac Lane

**Publisher:**

**ISBN:**

**Size**: 61.66 MB

**Format:**PDF

**Category :**Algebra, Homological

**Languages :**en

**Pages :**422

**View:**4835

**Book Description:**

## Homology Genes And Evolutionary Innovation

**Author**: Günter P. Wagner

**Publisher:**Princeton University Press

**ISBN:**0691180679

**Size**: 15.23 MB

**Format:**PDF, ePub

**Category :**Science

**Languages :**en

**Pages :**496

**View:**2858

**Book Description:**A major synthesis of homology, written by a top researcher in the field Homology—a similar trait shared by different species and derived from common ancestry, such as a seal's fin and a bird’s wing—is one of the most fundamental yet challenging concepts in evolutionary biology. This groundbreaking book provides the first mechanistically based theory of what homology is and how it arises in evolution. Günter Wagner, one of the preeminent researchers in the field, argues that homology, or character identity, can be explained through the historical continuity of character identity networks—that is, the gene regulatory networks that enable differential gene expression. He shows how character identity is independent of the form and function of the character itself because the same network can activate different effector genes and thus control the development of different shapes, sizes, and qualities of the character. Demonstrating how this theoretical model can provide a foundation for understanding the evolutionary origin of novel characters, Wagner applies it to the origin and evolution of specific systems, such as cell types; skin, hair, and feathers; limbs and digits; and flowers. The first major synthesis of homology to be published in decades, Homology, Genes, and Evolutionary Innovation reveals how a mechanistically based theory can serve as a unifying concept for any branch of science concerned with the structure and development of organisms, and how it can help explain major transitions in evolution and broad patterns of biological diversity.

## Cyclic Homology

**Author**: Jean-Louis Loday

**Publisher:**Springer Science & Business Media

**ISBN:**3662113899

**Size**: 10.54 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**516

**View:**3045

**Book Description:**From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.

## Cyclic Homology Of Extension Algebras With Application To Matrix Algebras Algebraic K Theory And Nest Algebras Of Operators

**Author**: Lars David Kadison

**Publisher:**

**ISBN:**

**Size**: 14.41 MB

**Format:**PDF, ePub

**Category :**

**Languages :**en

**Pages :**230

**View:**3964

**Book Description:**

## Analytic K Homology

**Author**: Nigel Higson

**Publisher:**OUP Oxford

**ISBN:**9780191589201

**Size**: 26.76 MB

**Format:**PDF, Kindle

**Category :**Mathematics

**Languages :**en

**Pages :**424

**View:**6954

**Book Description:**Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with specacular success to discover remarkable theorems across a wide span of mathematics. The purpose of this book is to acquaint the reader with the essential ideas of analytic K-homology and develop some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarse geometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C* - algebra theory, the book will lead the reader to some central notions of contemporary research in geometric functional analysis. Much of the material included here has never previously appeared in book form.

## Dihedral Homology And The Free Loop Space

**Author**: Gerald Matthew Lodder

**Publisher:**

**ISBN:**

**Size**: 32.55 MB

**Format:**PDF, ePub, Mobi

**Category :**

**Languages :**en

**Pages :**108

**View:**6048

**Book Description:**

## Elements Of Homology Theory

**Author**: Viktor Vasilʹevich Prasolov

**Publisher:**American Mathematical Soc.

**ISBN:**0821838121

**Size**: 22.20 MB

**Format:**PDF, ePub, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**418

**View:**1031

**Book Description:**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.