Math 544 References
The following books are on reserve in the
Math Library, and should be listed on the course reserve list
for Math 544.
- Lee, John M., Introduction to Topological Manifolds,
2nd. ed. (QA613.2 .L44 2011), our text.
Note that this is available as an e-book from the Math Library.
- Lee, John M., Introduction to Smooth Manifolds, 2nd. ed.
(QA613 .L44 2013), the text for 545/546.
Also available as an e-book from the Math Library.
- Bredon, Glen E., Topology and Geometry (QA612 .B74 1993),
intended as a first-year graduate text in algebraic topology.
Chapters I and III correspond to the syllabus for 544, and include many details
Bredon is very succinct, making this an excellent reference and second source,
but not always the most enlightening for a first exposure.
This book emphasizes manifolds (topological and smooth) throughout,
unlike other algebraic topology texts.
- Munkres, James R., Topology, 2nd. ed. (QA611 .M82 2000).
This is the text for our undergraduate and many other schools' undergraduate
and graduate topology courses. It has essentially everything we'll study
in 544, and most of the topics I'll mention that we have to omit.
Lots of interesting examples and problems.
(For homology, see Munkres's Elements of Algebraic Topology.)
- Sieradski, Allan J., An Introduction to Topology and Homotopy
(QA611 .S48 1992), starts with set theory and metric spaces, paced for an
undergraduate course, but gets through everything we'll discuss, including
a bit more along the way. Lots of examples and problems!
I've taught 544 from this book,
so likely will use some ideas and problems from it. Unfortunately sales were
not sufficient to support a second edition or even corrected printing: There
are a few mathematical errors in the problems, and a fair number of typos.
- Spivak, Michael, A Comprehensive Introduction to Differential
Geometry, Vol. I-V, 2nd ed. (QA641 .S59 1979).
The first volume is the most relevant
for 544. Reading Spivak is often like taking a bus tour,
viewing the scenery of differential topology and geometry but not stopping
at every sight to study it in detail. Sit down with a cup of coffee, or
perhaps even a glass of beer, to browse this book.
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Most recently updated on September 30, 2015.