๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Lehrbuch Der Topologie

โœ Scribed by Herbert Seifert, W. Threlfall


Book ID
127422886
Publisher
Chelsea Publishing Company
Year
2000
Tongue
German
Weight
5 MB
Edition
2nd
Category
Library
ISBN
0828400318
ASIN
B0017XE55U

No coin nor oath required. For personal study only.

โœฆ Synopsis


The 1930s were important years in the development of modern topology, pushed forward by the appearance of a few pivotal books, of which this is one. The focus is on combinatorial and algebraic topology, with as much point-set topology as needed for the main topics. One sees from the modern point of view that the authors are working in a category of spaces that includes locally finite simplicial complexes. (Their definition of manifold is more properly known today as a "triangulizable homology manifold".) Amazingly, they manage to accomplish a lot without the convenient tools of homological algebra, such as exact sequences and commutative diagrams, that were developed later. The main topics covered are: simplicial homology (coefficients in $\mathbb{Z}$ or $\mathbb{Z}_2$), local homology, surface topology, the fundamental group and covering spaces, three-manifolds, Poincarรฉ duality, and the Lefschetz fixed point theorem.

Few prerequisites are necessary. A final section reviews the lemmas and theorems from group theory that are needed in the text. As stated in the introduction to the important book by Alexandroff and Hopf (which appeared a year after Seifert and Threlfall): "Its lively and instructive presentation makes this book particularly suitable as an introduction or as a textbook."


๐Ÿ“œ SIMILAR VOLUMES


Lehrbuch der Topologie
โœ L. Vietoris ๐Ÿ“‚ Article ๐Ÿ“… 1937 ๐Ÿ› Springer Vienna ๐ŸŒ English โš– 72 KB
Topologie der Geschwรผlste
โœ Hans Gรผnther ๐Ÿ“‚ Article ๐Ÿ“… 1950 ๐Ÿ› Springer ๐ŸŒ English โš– 971 KB