Allen Hatcher

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Note: I have retired from teaching and advising students but am still active in research and writing. The best way to contact me is via email. If I do not respond in a timely fashion it is because I have nothing useful or definite to say.

Book Projects:
Course Notes:
Other Things:

Book Projects

Algebraic Topology

Alg Top Book Info This book, published in 2002, is a beginning graduate-level textbook on algebraic topology from a fairly classical point of view. To find out more or to download it in electronic form, follow this link to the download page.

VBKT Info Page Vector Bundles and K-Theory

This unfinished book is intended to be a fairly short introduction to topological K-theory, starting with the necessary background material on vector bundles and including also basic material on characteristic classes. For further information or to download the part of the book that is written, go to the download page.

Spectral Sequences

I have now returned to an earlier plan of having this material be an extra chapter of the Algebraic Topology book, rather than a separate book. The current version of this chapter is here. Its main focus is the Serre spectral sequence and its applications, but there is also some coverage of the Adams spectral sequence and, more briefly, a few other spectral sequences. In case you would like to see the older version that was planned as a separate book, this can be found on this page.

Topology of Numbers

This is an undergraduate-level introduction to elementary number theory from a somewhat geometric point of view, focusing on quadratic forms in two variables with integer coefficients. See the download page for more information and to get a pdf file of the book. Publication by the American Math Society is expected in 2022. The pdf version will remain freely available here after the print version appears.

List of Published Papers


Papers published since 1996:

Updates of older papers:

Unfinished drafts:

Unpublished papers:

Slides of Talks:

Photos of Renwick Brook