Essential Topology

Springer Undergraduate Mathematics Series

by Martin D. Crossley

Taking a direct route, "Essential Topology" brings the most important aspects of modern topology within reach of a second-year undergraduate student. It begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and the cornerstones of contemporary algebraic topology.
While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student.
With chapters continuity and topological spaces; deconstructionist topology; the Euler number; homotopy groups including the fundamental group; simplicial and singular homology, and fibre bundles.
"Essential Topology" contains enough material for two semester-long courses, and offers a one-stop-shop for undergraduate-level topology, leaving students motivated for postgraduate study in the field, and well-prepared for it.

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!