Four responses regarding texts................DMD ________________________________________ Subject: Re: photos and text request Date: Tue, 3 Apr 2001 12:16:59 -0400 (EDT) From: Dev Sinha As I think I've posted here before, I had a great time teaching first-year algebraic topology from Hatcher's book which is on the web at http://www.math.cornell.edu/~hatcher/ The content matches what Brayton mentioned, with some basic homotopy theory at the end if you make it that far. I like most if not all of the choices he made: starting with geometry but also developing the axiomatic viewpoint of homology for example, plenty of examples and problems, giving motivational discussion especially before long sections of rigorous development (for example at the beginning of doing homology), having "additional topics" sections from which one can pick and choose (I skipped most of them so I could do the Leray-Serre spectral sequence at the end of the year, which Hatcher has also written a bit about). Students liked the book a great deal - one phrase which comes to mind is "Hatcher's typically lucid style." Students also liked the fact that it is available free on the web (it will be available in print soon). -Dev > Subject: algebraic text > Date: Mon, 2 Apr 2001 19:49:27 -0500 (CDT) > From: Brayton Gray > > OK, how about suggestions for a text in algebraic topology. I am looking > for a text that will not get too technical too early and will have lots > of > concrete examples. Content: homology and cohomology possibly with the > fundamental group and covering spaces for starters. > > Brayton Gray > Math Department > UIC _____________________________________________ Subject: Re: 4 text suggestions Date: Tue, 03 Apr 2001 11:49:05 -0400 From: jim stasheff I am curious as to the thinking behind a point-set topology course at the undergrad level. The assumption is that this is what every potential grad student should know? An altrnative we have here has a minimum of point-set and then moves to surfaces and knots. jim ________________________________________ Subject: Re: photos and text request Date: Tue, 3 Apr 2001 10:10:39 -0500 (EST) From: James McClure I've been using a combination of Fulton's Algebraic Topology and Greenberg-Harper. Fulton's book begins by talking about line integrals and winding numbers and uses these to motivate 0- and 1-dimensional homology and (de Rham) cohomology of open sets in the plane. After about six weeks of this the students know the basic ideas of homology (chains, cycles and boundaries, duality between homology and cohomology, functoriality, homotopy invariance, the Meyer-Vietoris sequence) in low dimensions and then it's relatively straightforward to do Part II of Greenberg-Harper. Fulton also has the most complete treatment I know of the fundamental group and covering spaces. Jim McClure __________________________________________ Subject: Re: photos and text request Date: Tue, 3 Apr 2001 15:40:23 PST From: Kevin Iga To: dmd1@lehigh.edu (Don Davis) Some algebraic topology book suggestions: 1. Munkres, "Elements of Algebraic Topology" (Addison Wesley) Starts with simplicial homology, with lots of examples using surfaces, doing explicit computation. After that it gets more theoretical. Later covers singular homology and cohomology, Eilenberg-Steenrod axioms, duality theorems, universal coefficient theorems, etc. with an extra emphasis on acyclic models. Introduces algebraic machinery like diagram chasing and Ext functors when they are motivated by the topological need. 2. Hocking and Young, "Topology" (Dover) I mentioned this in the previous email. It does homology, in a similar way to Munkres, but not as many examples. 3. Kinsey "Topology of Surfaces" (Springer Verlag Undergrad Texts in Math) The easiest of the three books. Everything is motivated by the example of surfaces, and there are lots of examples everywhere using surfaces. Gives a good intuition about homology, but it doesn't get very far. DeRham cohomology is the only kind of cohomology mentioned, and it comes up only at the very end of the book. There is no singular homology approach, Mayer-Vietoris, or category theory. It does a good job at keeping it interesting, though, by demonstrating lots of cool results along the way. The discussion is very friendly and readable. Kevin Iga kiga@pepvax.pepperdine.edu