Essential Topology

Springer Undergraduate Mathematics Series

by Martin D. Crossley

This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

Genres: Mathematics, Science, Geometry

234 pages, Paperback

First published July 1, 2005

Reviews

[George Law · Rating 5 out of 5]

This excellent book is divided into two main parts. The first part develops general notions in point-set topology, particularly the ones that will be needed in the second part. The second part is about algebraic topology, of which three main areas are explored: homotopy, simplicial homology (divided into the homology of non-oriented simplices and of oriented simplices), and singular homology. Crossley has an excellent way of explaining concepts in this fascinating but often difficult subject, using informal examples and diagrams to help the reader understand better.

[Robert · Rating 4 out of 5]

Much clearer than any other topology books I've seen with the possible exception of Michael Henle's "Combinatorial Topology".

I really like the style and in fact the entire "Springer Undergraduate Mathematics Series".

It's about as gentle as you could find with all the things you could typically want, plenty of examples, explanations and exercises with a clear emphasis on key concepts and lots of motivation.

Now this came out a while ago so perhaps there is something newer and better, but on the other hand the basics haven't changed, so it should still be good!