Quinton Westrich
Teaching -> Topology SEP Summer 2016

The Topology SEP course is a short 5 week course designed to help graduate students prepare for the Topology Qualifying Exam at UW.

Week 1 Fundamental Group
Week 2 Homology
Week 3 Smooth Manifolds
Week 4 Cohomology
Week 5 Homotopy Theory

I take requests! Email me (my last name)@math.wisc.edu a few days in advance if you'd like to see a particular problem worked!

Links to Qualifying Exams and Info

August 1994-Jan 2010- with solutions!

All Past Quals- math library archive, no solutions

Official Info About the Quals

Spring 2016 Math 752 Webpage- try the HW and final!

Reference Handouts

Warning! All spaces are assumed to be nice (Hausdorff, T-everything, path-connected, locally path-connected, semi-locally simply connected...) unless the assumptions are explicitly weakened in the statements! The point is to understand the guts of theorems, the large hammers we'll use to hit tricky problems.

Fundamental Constructions: [pdf]- from Hatcher Ch.0

Fundamental Group: [pdf]- from Hatcher Ch.1 Sec.1-2

Covering Spaces: [pdf]- from Hatcher Ch.1 Sec. 3

Homology: [pdf]- from Hatcher Ch.2

Smooth Manifolds: [pdf]- from Spivak and (John) Lee

Cohomology: [pdf]- from Hatcher Ch.3

Problem Sets

Day 1 Problems: [pdf]- cell complexes, fundamental group, Van Kampen, gluing 2-cells

Day 2 Problems: [pdf]- covering spaces, Deck transformations

Day 3 Problems: [pdf]- LES of pairs, excision, Mayer-Vietoris, degrees, cellular homology

Day 4 Problems: [pdf]- cellular homology, lens spaces

Day 5 Problems: [pdf]- smooth manifolds

Solutions to Problem Sets
Contact

Office: 816 Van Vleck Hall
Department of Mathematics
Van Vleck Hall / 480 Lincoln Dr.
University of Wisconsin - Madison
Madison, WI 53706-1388
(my last name)@math.wisc.edu