Homotopical topology / by Anatoly Fomenko, Dmitry Fuchs.

Format:

Book

Author/Creator:

Fomenko, A. T., Author.

Fuks, D. B., Author.

Series:

Graduate texts in mathematics, 0072-5285 ; 273

Graduate Texts in Mathematics, 0072-5285 ; 273

Language:

English

Subjects (All):

Categories (Mathematics).

Algebra, Homological.

K-theory.

Algebraic topology.

Category Theory, Homological Algebra.

K-Theory.

Algebraic Topology.

Local Subjects:

Category Theory, Homological Algebra.

K-Theory.

Algebraic Topology.

Physical Description:

1 online resource (XI, 627 p. 210 illus.)

Edition:

Second edition

Place of Publication:

Cham : Springer International Publishing [2016].

Summary:

This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader’s mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A. T. Fomenko artistically render the wondrous beauty, and mystery, of the subject.

Contents:

Introduction

Homotopy

Homology

Spectral Sequences of Fibrations

Cohomology Operations

The Adams Spectral Sequence

K-Theory and Other Extraordinary Cohomology Theories.

ISBN:

3-319-23488-9