Basic topology. 3, Algebraic topology and topology of fiber bundles / Mahima Ranjan Adhikari.
Adhikari, Mahima Ranjan, author.
2022
QA612
Available Online

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Title Basic topology. 3, Algebraic topology and topology of fiber bundles / Mahima Ranjan Adhikari.
Author Adhikari, Mahima Ranjan, author.
ISBN 9789811665509 (electronic bk.)
9811665508 (electronic bk.)
9811665494
9789811665493
DOI https://doi.org/10.1007/978-981-16-6550-9
Published Singapore : Springer, 2022.
Language English
Description 1 online resource (xxv, 468 pages) : illustrations (some color)
Item Number 10.1007/978-981-16-6550-9 doi
Call Number QA612
Dewey Decimal Classification 514/.2
Summary This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 22, 2023).
Available in Other Form Print version: 9789811665493
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1. Prerequisite Concepts of Topology, Algebra and Category Theory
2. Homotopy Theory: Fundamental and Higher Homotopy Groups
3. Homology and Cohomology Theories: An Axiomatic Approach with Consequences
4. Topology of Fiber Bundles
5. Homotopy Theory of Bundles
6. Some Applications of Algebraic Topology
7. Brief History on Algebraic Topology and Fiber Bundles.

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