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＜電子ブック＞
Algebraic Topology : A First Course / by William Fulton
(Graduate Texts in Mathematics. ISSN:21975612 ; 153)

版	1st ed. 1995.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1995
本文言語	英語
大きさ	XVIII, 430 p. 13 illus : online resource
冊子体	Algebraic topology : a first course / William Fulton ; : us - : gw : pbk
著者標目	*Fulton, William author SpringerLink (Online service)
件　名	LCSH:Topology FREE:Topology
一般注記	I Calculus in the Plane -- 1 Path Integrals -- 2 Angles and Deformations -- II Winding Numbers -- 3 The Winding Number -- 4 Applications of Winding Numbers -- III Cohomology and Homology, I -- 5 De Rham Cohomology and the Jordan Curve Theorem -- 6 Homology -- IV Vector Fields -- 7 Indices of Vector Fields -- 8 Vector Fields on Surfaces -- V Cohomology and Homology, II -- 9 Holes and Integrals -- 10 Mayer—Vietoris -- VI Covering Spaces and Fundamental Groups, I -- 11 Covering Spaces -- 12 The Fundamental Group -- VII Covering Spaces and Fundamental Groups, II -- 13 The Fundamental Group and Covering Spaces -- 14 The Van Kampen Theorem -- VIII Cohomology and Homology, III -- 15 Cohomology -- 16 Variations -- IX Topology of Surfaces -- 17 The Topology of Surfaces -- 18 Cohomology on Surfaces -- X Riemann Surfaces -- 19 Riemann Surfaces -- 20 Riemann Surfaces and Algebraic Curves -- 21 The Riemann—Roch Theorem -- XI Higher Dimensions -- 22 Toward Higher Dimensions -- 23 Higher Homology -- 24 Duality -- Appendices -- Appendix A Point Set Topology -- A1. Some Basic Notions in Topology -- A2. Connected Components -- A3. Patching -- A4. Lebesgue Lemma -- Appendix B Analysis -- B1. Results from Plane Calculus -- B2. Partition of Unity -- Appendix C Algebra -- C1. Linear Algebra -- C2. Groups; Free Abelian Groups -- C3. Polynomials; Gauss’s Lemma -- Appendix D On Surfaces -- D1. Vector Fields on Plane Domains -- D2. Charts and Vector Fields -- D3. Differential Forms on a Surface -- Appendix E Proof of Borsuk’s Theorem -- Hints and Answers -- References -- Index of Symbols To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re­ lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ­ ential topology, etc.), we concentrate our attention on concrete prob­ lems in low dimensions, introducing only as much algebraic machin­ ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol­ ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel­ opment of the subject. What would we like a student to know after a first course in to­ pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under­ standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind­ ing numbers and degrees of mappings, fixed-point theorems; appli­ cations such as the Jordan curve theorem, invariance of domain; in­ dices of vector fields and Euler characteristics; fundamental groups Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-4180-5

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