William S. Massey

A Basic Course in Algebraic Topology

• Gebundenes Buch

Produktbeschreibung

This book is intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized. The text consists of material from the first five chapters of the author's earlier book, ALGEBRAIC TOPOLOGY: AN INTRODUCTION (GTM 56), together with almost all of the now out-of- print SINGULAR HOMOLOGY THEORY (GTM 70). The material from the earlier books has been carefully revised, corrected, and brought up to date.

Produktdetails

• Graduate Texts in Mathematics 127
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 10030942, 978-0-387-97430-9
• 1991
• Seitenzahl: 452
• Erscheinungstermin: 6. März 1991
• Englisch
• Abmessung: 241mm x 160mm x 30mm
• Gewicht: 783g
• ISBN-13: 9780387974309
• ISBN-10: 038797430X
• Artikelnr.: 21703958

Autorenporträt

William S. Massey (1920-2017) was an American mathematician known for his work in algebraic topology. The Blakers-Massey theorem and the Massey product were both named for him. His textbooks Singular Homology Theory  and Algebraic Topology: An Introduction are also in the Graduate Texts in Mathematics series.

Inhaltsangabe

1: Two-Dimensional Manifolds .- 2: The Fundamental Group .- 3: Free Groups and Free Products of Groups.- 4: Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications .- 5: Covering Spaces .- 6: Background and Motivation for Homology Theory .- 7: Definitions and Basic Properties of Homology Theory .- 8: Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory .- 9: Homology of CW-Complexes.- 10: Homology with Arbitrary Coefficient Groups .- 11: The Homology of Product Spaces.- 12: Cohomology Theory.- 13: Products in Homology and Cohomology.- 14: Duality Theorems for the Homology of Manifolds.- 15: Cup Products in Projective Spaces and Applications of Cup Products. Appendix A: A Proof of De Rham's Theorem..- Appendix B: Permutation Groups or Tranformation Groups.