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. (As of 9/30: Spivak books are on reserve, but for some reason not yet on list for course.)

• 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; search via course reserves, or restricted to UW holdings, so you get to the UW's copy (and aren't asked to pay). If you have difficulty using e-books from an off-campus computer, on the library webpage go to "Help & Support: Off-Campus Access and Technical Support" and follow instructions.
  I will assume you have entered all important corrections in your copy of the text.
  Please report any additional errors you suspect to me or directly to Professor Lee.
• Lee, John M., Introduction to Smooth Manifolds, 2nd. ed. (QA613 .L44 2013), the text for 545/546.
• 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 we skip. As this suggests, 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 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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