9781466562431-1466562439-Basic Algebraic Topology

Basic Algebraic Topology

ISBN-13: 9781466562431
ISBN-10: 1466562439
Edition: 1
Author: Shastri, Anant R.
Publication date: 2013
Publisher: Chapman and Hall/CRC
Format: Hardcover 551 pages
FREE shipping on ALL orders

Book details

ISBN-13: 9781466562431
ISBN-10: 1466562439
Edition: 1
Author: Shastri, Anant R.
Publication date: 2013
Publisher: Chapman and Hall/CRC
Format: Hardcover 551 pages

Summary

Acknowledged authors Shastri, Anant R. wrote Basic Algebraic Topology comprising 551 pages back in 2013. Textbook and eTextbook are published under ISBN 1466562439 and 9781466562431. Since then Basic Algebraic Topology textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology.

The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and simplicial complexes. It then focuses on the fundamental group, covering spaces and elementary aspects of homology theory. It presents the central objects of study in topology visualization: manifolds. After developing the homology theory with coefficients, homology of the products, and cohomology algebra, the book returns to the study of manifolds, discussing Poincaré duality and the De Rham theorem. A brief introduction to cohomology of sheaves and Čech cohomology follows. The core of the text covers higher homotopy groups, Hurewicz’s isomorphism theorem, obstruction theory, Eilenberg-Mac Lane spaces, and Moore-Postnikov decomposition. The author then relates the homology of the total space of a fibration to that of the base and the fiber, with applications to characteristic classes and vector bundles. The book concludes with the basic theory of spectral sequences and several applications, including Serre’s seminal work on higher homotopy groups.

Thoroughly classroom-tested, this self-contained text takes students all the way to becoming algebraic topologists. Historical remarks throughout the text make the subject more meaningful to students. Also suitable for researchers, the book provides references for further reading, presents full proofs of all results, and includes numerous exercises of varying levels.

Rate this book Rate this book

We would LOVE it if you could help us and other readers by reviewing the book