Homology

Author : James W. Vick
Publisher : Springer Science & Business Media
ISBN 13 : 1461208815
Total Pages : 258 pages
Book Rating : 4.15/5 ( download)

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Download or read book Homology Theory written by James W. Vick and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Peter S. Ozsváth
Publisher : American Mathematical Soc.
ISBN 13 : 1470417375
Total Pages : 410 pages
Book Rating : 4.76/5 ( download)

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Download or read book Grid Homology for Knots and Links written by Peter S. Ozsváth and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3662217392
Total Pages : 467 pages
Book Rating : 4.99/5 ( download)

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Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Author : Saunders MacLane
Publisher : Springer Science & Business Media
ISBN 13 : 3642620299
Total Pages : 436 pages
Book Rating : 4.94/5 ( download)

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Download or read book Homology written by Saunders MacLane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

Author : Günter P. Wagner
Publisher : Princeton University Press
ISBN 13 : 0691180679
Total Pages : 494 pages
Book Rating : 4.70/5 ( download)

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Download or read book Homology, Genes, and Evolutionary Innovation written by Günter P. Wagner and published by Princeton University Press. This book was released on 2018-07-10 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jean-Claude Hausmann
Publisher : Springer
ISBN 13 : 3319093541
Total Pages : 539 pages
Book Rating : 4.43/5 ( download)

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Download or read book Mod Two Homology and Cohomology written by Jean-Claude Hausmann and published by Springer. This book was released on 2015-01-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: 1. It leads more quickly to the essentials of the subject, 2. An absence of signs and orientation considerations simplifies the theory, 3. Computations and advanced applications can be presented at an earlier stage, 4. Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book.

Author : Peter Giblin
Publisher : Cambridge University Press
ISBN 13 : 1139491172
Total Pages : 273 pages
Book Rating : 4.74/5 ( download)

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Download or read book Graphs, Surfaces and Homology written by Peter Giblin and published by Cambridge University Press. This book was released on 2010-08-12 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.

Author : Tomasz Kaczynski
Publisher : Springer Science & Business Media
ISBN 13 : 0387215972
Total Pages : 488 pages
Book Rating : 4.76/5 ( download)

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Download or read book Computational Homology written by Tomasz Kaczynski and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

Author : Lewis I. Held, Jr
Publisher : Cambridge University Press
ISBN 13 : 1316982718
Total Pages : 291 pages
Book Rating : 4.16/5 ( download)

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Download or read book Deep Homology? written by Lewis I. Held, Jr and published by Cambridge University Press. This book was released on 2017-01-28 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Humans and flies look nothing alike, yet their genetic circuits are remarkably similar. Here, Lewis I. Held, Jr compares the genetics and development of the two to review the evidence for deep homology, the biggest discovery from the emerging field of evolutionary developmental biology. Remnants of the operating system of our hypothetical common ancestor 600 million years ago are compared in chapters arranged by region of the body, from the nervous system, limbs and heart, to vision, hearing and smell. Concept maps provide a clear understanding of the complex subjects addressed, while encyclopaedic tables offer comprehensive inventories of genetic information. Written in an engaging style with a reference section listing thousands of relevant publications, this is a vital resource for scientific researchers, and graduate and undergraduate students.

Author : W.S. Massey
Publisher : Springer Science & Business Media
ISBN 13 : 1468492314
Total Pages : 278 pages
Book Rating : 4.16/5 ( download)

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Download or read book Singular Homology Theory written by W.S. Massey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on homology and cohomology theory is geared towards the beginning graduate student. Singular homology theory is developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind various algebraic concepts is emphasized. The only formal prerequisites are knowledge of the basic facts of abelian groups and point set topology. Singular Homology Theory is a continuation of t he author's earlier book, Algebraic Topology: An Introduction, which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding Singular Homology Theory.