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Basic Algebraic Topology

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by Anant R. Shastri
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Basic Algebraic Topology by Anant R. Shastri

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 ?ech 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.To view this DRM protected ebook on your desktop or laptop you will need to have Adobe Digital Editions installed. It is a free software. We also strongly recommend that you sign up for an AdobeID at the Adobe website. For more details please see FAQ 1&2. To view this ebook on an iPhone, iPad or Android mobile device you will need the Adobe Digital Editions app, or BlueFire Reader or Txtr app. These are free, too. For more details see this article.

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Ebook Details
Pages: 551
Size: 6.2 MB
Publisher: CRC Press
Date published:   2013
ISBN: 9781466562448 (DRM-PDF)

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This product is listed in the following categories:

Nonfiction > Mathematics > Algebra
Nonfiction > Mathematics > Geometry

This author has products in the following categories:

Nonfiction > Mathematics > Geometry
Nonfiction > Mathematics > Algebra

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