Ma 151a, Algebraic and Geometric Topology

Fall 2006

Course Description

Math 151 is the year-long graduate sequence in topology and geometry. In the first term, we'll cover the fundamental group, homology, and some basics of manifold topology. Basically, we'll cover Chapters 0-2 of the required text, which is

Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002. ISBN: 0521795400

You can download the full text here, but you'll probably want to actually buy it – it's only $32 for 500+ pages. (A useful list of errata is also available.)

As for prerequisites, you should have a good understanding of basic point-set topology. In addition, I will cover the initial aspects of the fundamental group quite quickly, on the presumption that most of you have seen this already. Those students not familiar with the fundamental group should look over Section 1.1 of Hatcher prior to the start of class. Here at Caltech, Ma 109a is sufficient background for this class.


Details: Your grade in the course will be based on the weekly homework (50%), the midterm (20%) and the final (30%). Letter grades will be given, unless you specifically tell the Registrar that you want to be graded Pass/Fail.

The weekly homework will be due in class on Fridays, at the beginning of class. (Here "beginning of class" will be interpreted generously, say up to 10 minutes after I start, so no need to rush if your running a bit late.) Homework turned in after that, up through the beginning of class on Monday, will be graded but only count for half-credit. Beyond this, late homework will not be accepted, except in certain extreme circumstances, in which case you must ask me for an extension prior to the due date. However, your lowest homework grade will be dropped. If you won't be in class on Friday, turn your homework into my box outside the math department office at least 15 minutes prior to the start of class; late-but-not-too-late HW can be put in the same place. As Friday November 24th is a holiday, HW#9 will instead be due on Wednesday, November 29th.

You are allowed, nay encouraged, to work with other people on the HW. However, you must write up your answers individually, and credit your collaborators. However, no collaboration is allowed on the exams.

The midterm will replace the 6th homework set, and thus be due on Friday, November 5th. It will given out during class on October 29th, and, beyond that, will not be time restricted.

The final will be handed out in class on Wednesday, November 29 and due at a time to be determined on Thursday, December 7th. Like the midterm, it will not be otherwise time restricted.

Homework Assignments

All problem numbers refer to Hatcher's book.

Lecture Notes

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