Algebraic Topology

A First Course

William Fulton (Autor)

Buch | Softcover

452 Seiten

1995 | 1995
Springer US (Verlag)
978-3-540-94327-3 (ISBN)

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This book introduces the important ideas of algebraic topology emphasizing the relation of these ideas with other areas of mathematics. Rather than choosing one point of view of modern topology (homotopy theory, axiomatic homology, or differential topology, say) the author concentrates on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts; it is also in harmony with the historical development of the subject. The book is aimed at students who do not necessarily intend on specializing in algebraic topology. The first part of the book emphasizes relations with calculus and uses these ideas to prove the Jordan curve theorem. The study of fundamental groups and covering spaces emphasizes group actions. A final section gives a taste of the generalization to higher dimensions. This book introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. Rather than choosing one point of view of modern topology (homotropy theory, axiomatic homology, or differential topology, say) the author concentrates on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts; it is also in harmony with the historical development of the subject. The book is aimed at students who do not necessarily intend on specializing in algebraic topology.

Preface.- Calculus in the Plane.- Winding Numbers.- Cohomology and Homology, I.- Vector Fields.- Cohomology and Homology, II.- Covering Spaces and Fundamental Groups, I.- Covering Spaces and Fundamental Groups, II.- Cohomology and Homology, III.- Topology of Surfaces.- Riemann Surfaces.- Higher Dimensions.- Appendices.

Erscheinungsdatum	19.03.2022
Reihe/Serie	Graduate Texts in Mathematics
Sprache	englisch
Maße	155 x 235 mm
Gewicht	680 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	3-540-94327-7 / 3540943277
ISBN-13	978-3-540-94327-3 / 9783540943273
Zustand	Neuware