Meeting times: MWF, 11:00am11:50am (MTH 0104)
Instructor: Professor Jonathan
Rosenberg. His office is room 2114 of the Math Building,
phone extension 55166, or you can contact him by
email. His office hours
are Mondays 910 and Fridays 12, or by appointment.
Homework grader: Krishna Kaipa, office in
room 4410 of the Math Building.
Texts: Topology and Geometry by Glen E. Bredon, Graduate Texts in Math., vol. 139, SpringerVerlag, Corrected 3rd Printing, 1997, ISBN 9780387979267, and Algebraic Topology by Allen Hatcher, available free on the web, also published by Cambridge University Press in a paperback edition (ISBN 9780521795401) at $35. If you want still another reference that's not too expensive, I'd recommend A Concise Course in Algebraic Topology by J. Peter May, Chicago Lectures in Math., Univ. of Chicago Press, 1999, ISBN 9780226511832, for $22. This book is also available on the web. It's rather terse but covers everything.
Prerequisite: MATH 403 (undergraduatelevel abstract algebra). MATH 730 or equivalent is recommended, not 100% necessary if you are willing to take a few facts about the fundamental group on faith.
Catalog description: Singular homology and cohomology, cup products, Poincaré duality, EilenbergSteenrod axioms, Whitehead and Hurewicz theorems, universal coefficient theorem, cellular homology.
Basically, we will cover most of Chapters IV, V, and VI of Bredon, with some of the "starred sections" omitted. Much of this material is also in Hatcher, Ch. 23, with a slightly different point of view, and you might find a second presentation helpful.
Homework will be assigned, collected, and graded, usually once a week. In addition, there will be a midsemester exam and a 2hour final exam. This course is designed to prepare students for the second half of the graduate qualifying exam in Geometry/Topology. Thus grades will have the following meaning:
Please fill out the course evaluation questionnaire between Tuesday, April 29 and Wednesday, May 14th.
(Some details to be filled in later if necessary)
Week  Material Covered (Reading Assignment)  Homework and Special Notes  
Week of January 28  Bredon, Ch. IV, sections 13. Also see Hatcher, pp. 97110.  Due Monday, Feb. 4:


Week of February 4  Bredon, Ch. IV, sections 46  Due Monday, Feb. 11: Assignment 2  
Week of February 11  Bredon, Ch. IV, sections 15, 78  Due Monday, Feb. 18: Hatcher, Ch. 2, p. 132, exercise 22, and pp. 155156, exercises 4, 8, 12. In these problems, assume that singular homology satisfies the axioms.  
Week of February 18  Bredon, Ch. IV, sections 911  Due Monday, Feb. 25: Bredon, p. 206, #4, 5, 6, 7, and p. 211, #4 (in fact, show it's finitely presented, i.e., is given by finitely many generators and finitely many relations).  
Week of February 25  Bredon, Ch. IV, sections 1214, 16  Due Monday, March 3:


Week of March 3  Bredon, Ch. IV, sections 1719. Also see Hatcher, pp. 99126.  Due Monday, March 10: Do the problems in Hatcher, p. 133, #26 and p. 158, #33.  
Week of March 10  Bredon, Ch. IV, sections 1920. Also see Hatcher, pp. 177184.  No homework this week because of midterm exam and spring break.  
Friday, March 14  Midterm Exam on Bredon, Ch. IV, and Hatcher, Ch. 2.  For help in studying, see this old exam with solutions.  
Week of March 17  Spring Break, No Class  
Week of March 24  Bredon, Ch. IV, sections 2123; Hatcher, pp. 177184.  Due Monday, March 31: Bredon, p. 250, #13; p. 259, #4.  
Week of March 31  Bredon, Ch. V, sections 15  Due Monday, April 7:


Week of April 7  Bredon, Ch. V, sections 68.  Due Monday, April 14:


Week of April 14  Bredon, sections 910 (cont'd); Ch. VI, sections 12. 
Due Wednesday, April 23:


Week of April 21  Bredon, Ch. VI, sections 25; Hatcher, pp. 206217.  Due Wednesday, April 30:


Week of April 28  Bredon, Ch. VI, sections 68.  Due Wednesday, May 7:


Weeks of May 5, May 12  Bredon, Ch. VI, sections 911.  May 12 is day of last class.  
Rescheduled to Thursday, May 15, 10:0012:00 am, usual room (MTH 0104)  Final Exam. For help in studying, here are a recent final exam and an old final exam. The latter dates to a time when we used a different textbook, but the topics covered are pretty much the same.  Special PreExam Office Hours: Wed., May 14, 24 PM  
This year's exams and solutions have been uploaded to the departmental testbank. 