A History of Algebraic and Differential Topology, 1900 - 1960

1. Auflage 1989. Softcover printing of hardcover Auflage. 2009
ISBN: 978-0-8176-4906-7
Verlag: Birkhauser Boston

Buch, Englisch, 648 Seiten, Format (B × H): 156 mm x 235 mm, Gewicht: 2050 g

Reihe: Modern Birkhäuser Classics

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results. Within its chosen boundaries the coverage of this book is superb. Read it!

—MathSciNet

Zielgruppe

Research

Autoren/Hrsg.

Dieudonné, Jean

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Simplicia1 Techniques and Homology.- The Work of Poincar#x00E9;.- The Build-Up of #x201C;Classical#x201D; Homology.- The Beginnings of Differential Topology.- The Various Homology and Cohomology Theories.- The First Applications of Simplicia1 Methods and of Homology.- The Concept of Degree.- Dimension Theory and Separation Theorems.- Fixed Points.- Local Homological Properties.- Quotient Spaces and Their Homology.- Homolagy of Groups and Homogeneous Spaces.- Applications of Homology to Geometry and Analysis.- Homotopy and its Relution to Homology.- Fundamental Group and Covering Spaces.- Elementary Notions and Early Results in Homotopy Theory.- Fibrations.- Homology of Fibrations.- Sophisticated Relations between Homotopy and Homology.- Cohomology Operations.- Generalized Homology and Cohomology.