Revisions, Additions, and Alternative Versions for Algebraic Topology

These are potential revisions to the first edition of the book. Clicking on the link downloads a pdf version of the file.

• Additional Exercises: Approximately 80 new exercises, along with enhanced versions of a few of the original exercises. This brings the total number of exercises in the book to over 500.
• A house with one room: A simpler version of the house with two rooms described on page 4. It happens to be homeomorphic to a space commonly called the dunce hat.
• An extra page: For the end of Section 1.2, making explicit the fact that the fundamental group of a CW complex depends only on its 2-skeleton.
• Section 1.3: An alternative arrangement of the material on covering spaces, emphasizing group actions more.
• Delta Complexes: An improved definition of Delta Complexes, pp. 102-104 of Section 2.1. This has now been incorporated into later printings of the book (since 2006) and the online version.
• Section 3.2: Mainly a rearrangement of the middle of this section on cup products into an order that seems slightly more efficient.
• Proposition 3.22: This includes a proof for n odd as well as n even.
• Lemma 3.27: A slightly simplified statement, with corresponding minor changes in the proof. (This revision has been incorporated into the second and later printings of the book.)
• Cap Products: A new version of the exposition on pages 239-242 that emphasizes the connection with cup products. There are also smaller changes on pages 248-250. The pdf file includes the pages in between as well, but these are unchanged.
• Lemma 4.10: A cleaner statement and proof. (This has been incorporated into the online version.)
• CW Approximations: A rearrangement of pp. 352-355, to improve the exposition.
• Appendix: This adds a little more point-set topology: a new Proposition A.17 relating product and quotient spaces, and an example of Dowker about products of CW complexes. The proof that Delta complexes are CW complexes on pp.519-520 has been deleted since this is now unnecessary with the revised definition of Delta complexes given on the new pp.102-104. (This revision has been incorporated into the online version.)
• Simplicial Structures on CW Complexes: A five-page addition to the Appendix which discusses special classes of CW complexes that are provided with various sorts of simplicial structures. In particular, simplicial sets are introduced and related to the CW complexes which are their geometric realizations. (My thanks to Greg Kuperberg for telling me about this geometric view of simplicial sets.)