Introduction to Algebraic Topology

Language: English

Published by Springer, 2022

3030983129 / 9783030983123

Series: Book 32 of 32 - Compact Textbooks in Mathematics

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - 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 axiomsfor 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.

Seller Inventory # 9783030983123

Title
Introduction to Algebraic Topology
Author
Holger Kammeyer
Publisher
Springer
Publication year
2022
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3030983129
ISBN 13
9783030983123
Item weight
335 grams
Dimensions
235x155x11 mm
Series
Book 32 of 32: Compact Textbooks in Mathematics

AHA-BUCH GmbH

Einbeck, Germany

5-star seller

AbeBooks seller since August 14, 2006

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