Topology Qual Prep Summer 2009
Office: AP&M 6452
Office Hours: Tuesday 9/1 2-3 p.m.
Friday 9/4 2-3 p.m.
Monday 9/7 1-2 p.m.
Meeting Times: MWF 9:00 a.m. - 12:00 p.m.
We will meet in AP&M 5829 (the lecture room on the top floor of AP&M prime)
Monday and Wednesday formatted as follows:
20-30 minute quiz (1 or two questions) covering topics you learned last session
1 hour of lecture/explanation of techniques
The remaining time will be spent on exercises related to the weeks topics
Fridays will be used for practice quals. Most of the time will be spent taking the practice qual, to simulate
a real qual environment. The last 20 or 30 minutes of the session we will share our answers for the qual.
Qualifying Exam Syllabus:
(Implicitly Assumed: topological spaces, point set topology)
Fundamental group
Covering spaces
CW Complexes
Simplicial homology
Singular homology
Homology of spheres, degree of maps
Cellular computation of homology
Cohomology and products
Universal coefficient and Kunneth theorems
Manifolds
Poincare duality and its consequences
Homotopy groups
Whitehead theorem, Hurewicz theorem and their consequences