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＜E-Book＞
Algebraic Topology / by Clark Bray, Adrian Butscher, Simon Rubinstein-Salzedo

Edition	1st ed. 2021.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2021
Size	XIV, 209 p. 69 illus., 28 illus. in color : online resource
Authors	*Bray, Clark author Butscher, Adrian author Rubinstein-Salzedo, Simon author SpringerLink (Online service)
Subjects	LCSH:Algebraic topology LCSH:Group theory LCSH:Topological groups LCSH:Lie groups FREE:Algebraic Topology FREE:Group Theory and Generalizations FREE:Topological Groups and Lie Groups
Notes	Introduction -- 1. Surface Preliminaries -- 2. Surfaces -- 3. The Euler Characteristic and Identification Spaces -- 4. Classification Theorem of Compact Surfaces -- 5. Introduction to Group Theory -- 6. Structure of Groups -- 7. Cosets, Normal Subgroups, and Quotient Groups -- 8. The Fundamental Group -- 9. Computing the Fundamental Group -- 10. Tools for Fundamental Groups -- 11. Applications of Fundamental Groups -- 12. The Seifert-Van Kampen Theorem -- 13. Introduction to Homology -- 14. The Mayer-Vietoris Sequence -- A. Topological Notions -- Bibliography -- Index Algebraic Topology is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the preliminaries needed for the formal definition of a surface. Other topics covered in the book include the classification of surfaces, group theory, the fundamental group, and homology. This book assumes no background in abstract algebra or real analysis, and the material from those subjects is presented as needed in the text. This makes the book readable to undergraduates or high-school students who do not have the background typically assumed in an algebraic topology book or class. The book contains many examples and exercises, allowing it to be used for both self-study and for an introductory undergraduate topology course HTTP:URL=https://doi.org/10.1007/978-3-030-70608-1

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