Math 151 is the year-long graduate sequence in topology and geometry. The second term covers cohomology, homotopy theory, and (time permitting) spectral sequences. The first two topics are treated in Chapters 3 and 4 of
Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002.
This is the same textbook as last quarter. You can download the full text here. (A useful list of errata is also available.) In the event that we actually get to spectral sequences, appropriate references will be provided then.
Prerequisites: Ma 151a, or an equivalent course covering the contents of the first two chapters of Hatcher.
Short version: The same as last quarter.
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.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 collaboratoration is allowed on the exams.
The midterm will replace the 6th homework set, and thus be due on Friday, February 17th. It will given out during class on February 10th, and, beyond that, will not be time restricted.
The final will be handed out in class on Wednesday, March 8th and due at a time to be determined on Friday, March 17th. Like the midterm, it will not be otherwise time restricted.
All problem numbers refer to the Hatcher's book.