Math 971 - Algebraic Topology - Spring 2005 - Course Information

Section 1: TR 11:00-12:15 AvH 119
Instructor: Mark Brittenham
Office: 317 Avery Hall, 472-7222
Email: mbritten at math dot unl dot edu
Course web page: Link: mbritten/classwk/971s05/

Office hours: Tentatively: My office hours will be Tuesdays and Thursdays 9:30-10:30 (or by appointment) in Avery 317. The grader for Math 971, Steve Haataja, will hold hold office hours Mondays and Wednesdays 9:30-10:30 (or by appointment) in Avery 228.

Prerequisite: Math 970, or consent of instructor.

Course description: This course will give an overview of algebraic topology. We'll begin with an overview/review of several Math 970 topics, including quotient topology and homotopy (fundamental groups and covering spaces). We'll build on these, to develop methods to build topological spaces as cell complexes, to compute many fundamental groups with the Seifert-Van Kampen Theorem, and to classify covering spaces (the "Galois correspondence"). Next we'll cover the basics of homology, including using the Mayer-Vietoris Theorem to compute homology groups. As time permits, we'll also discuss topics in geometric/differential topology, in particular the study of manifolds.

Text: The textbook that we will primarily follow is Algebraic Topology by Allen Hatcher; we'll cover most of chapters 0-2 of that text. This book is available electronically at the author's web site, I recommend that you purchase the paperback version. The hardback version is on reserve in the math library (QA612 .H42 2002). I will supplement that text from time to time with material from other texts Susan placed on reserve in the math library: Topology, Second Edition, by James R. Munkres (QA611 .M82 2000) includes material on homotopy in chapters 9-14, and Elements of Algebraic Topology by James R. Munkres (QA612 .M86 1984) discusses homology theory in considerable depth.

Requirements: Each two weeks or so I will be assigning some homework problems; a subset of the problems will be marked out to be handed in. These will vary in difficulty from easy to the size of a small project (expect a few of this size). For those that are not handed in, I will expect you to discuss answers in class. You may work on the homework in groups if you wish, although I recommend that you each try the problems and proofs individually before talking them over with other people. When it is written, the homework must be written up individually, even if the problems are solved by a group of students - several identical copies of the same solutions will not be accepted. Late homework won't be accepted, but the two lowest homework grades will be dropped. The grade for the course will be based completely on the homework.

Notes: I'd like to encourage you to ask questions during lectures. At the beginning of each class, if you have a question on the material we've covered so far, or if you're thoroughly stuck on a homework problem, please feel free to ask about it. If I say something confusing during the class, also please let me know. I very much prefer lectures to be interactive.

Miscellaneous legal stuff: Students who believe their academic evaluation has been prejudiced or capricious have recourse for appeals to (in order) the instructor, the departmental chair, the departmental appeals committee, and the college appeals committee.
Friday, January 21 is the last day to drop a course and not have it appear on your transcript. Friday, March 4 is the last day to change a course registration to or from ``Pass/No Pass''. Friday, April 8 is the last day to drop a course with a grade of W (withdrawal).

M. Brittenham