A First Course in Geometric Topology and Differential Geometry

by Ethan D. Bloch

The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship between modern axiomatic approach and geometric intuition. The text is kept at a concrete level, 'motivational' in nature, avoiding abstractions. A number of intuitively appealing definitions and theorems concerning surfaces in the topological, polyhedral, and smooth cases are presented from the geometric view, and point set topology is restricted to subsets of Euclidean spaces. The treatment of differential geometry is classical, dealing with surfaces in R3 . The material here is accessible to math majors at the junior/senior level.

Genres: Mathematics

433 pages, Hardcover

First published December 1, 1996

Reviews

[Didier "Dirac Ghost" Gaulin · Rating 3 out of 5]

A very intuitive and concept heavy text on geometric topology, the topological equivalence to differential geometry. The concept and gluing algorithms are very well explained, detailed and done step by step. Since it is beginner friendly, certain definitions (the definition of orientability comes to mind) are a little bit too simplified. My second slightly negative critic of the text is that certain proofs are rather inelegant or unfinished. Still, it is a very good companion text for those who prefer the topological path to the analytical one.