Name: Introduction to Algebraic Topology
Brand: Springer Verlag
SKU: 9783030983123
Price: 3137.0 INR
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Introduction to Algebraic Topology

by Holger Kammeyer

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ISBN13: 9783030983123
Binding: Paperback
Subject: Mathematics and Statistics
Publisher: Springer Verlag
Publisher Imprint: Springer
Publication Date: October 16, 2022
Pages: 182
Original Price: EUR 44.99
Language: English
Edition: N/A
Item Weight: 270 grams
BISAC Subject(s): Topology

About The Book

This textbook provides a succinct introduction to algebraic topology. It follows a modern categorical approach from the beginning and gives ample motivation throughout so that students will find this an ideal first encounter to the field. Topics are treated in a self-contained manner, making this a convenient resource for instructors searching for a comprehensive overview of the area. It begins with an outline of category theory, establishing the concepts of functors, natural transformations, adjunction, limits, and colimits. As a first application, van Kampen's theorem is proven in the groupoid version. Following this, an excursion to cofibrations and homotopy pushouts yields an alternative formulation of the theorem that puts the computation of fundamental groups of attaching spaces on firm ground. Simplicial homology is then defined, motivating the Eilenberg-Steenrod axioms, and the simplicial approximation theorem is proven. After verifying the axioms for singular homology, various versions of the Mayer-Vietoris sequence are derived and it is shown that homotopy classes of self-maps of spheres are classified by degree.The final chapter discusses cellular homology of CW complexes, culminating in the uniqueness theorem for ordinary homology. Introduction to Algebraic Topology is suitable for a single-semester graduate course on algebraic topology. It can also be used for self-study, with numerous examples, exercises, and motivating remarks included.

About The Author

Holger Kammeyer is Assistant Professor of Algebra and Geometry at the University of Düsseldorf. His research interests include algebraic topology as well as arithmetic and profinite groups. A particular field of his expertise is the theory of ℓ²-invariants on which he has authored the textbook Introduction to ℓ²-invariants (Lecture Notes in Mathematics, Volume 2247, Springer).

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