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!

**August 1994-Jan 2010**- with solutions!

**All Past Quals**- math library archive, no solutions

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

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

**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

**Day 3 Problem Solutions**: [pdf]

**Day 5 Problem Solutions**: [pdf]

**Day 8 Problem Solutions**: [pdf]

Please email errata to (my last name)@math.wisc.edu

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