William Fulton

Algebraic Topology

A First Course

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Graduate Texts in Mathematics Vol.153
• Verlag: Springer, Berlin
• 1995.
• Seitenzahl: 452
• Erscheinungstermin: 27. Juli 1995
• Englisch
• Abmessung: 235mm x 155mm x 25mm
• Gewicht: 640g
• ISBN-13: 9783540943273
• ISBN-10: 3540943277
• Artikelnr.: 05685938

Inhaltsangabe

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.