Topology ---Information on semester project
NOTE: Added: Since nobody indicated by the deadline that they would be doing a project, this option is no longer available as originally
offered.
In the final weeks of the semester you will be given time to work on a project.
You may choose one of the following options:
1) The default option is simplicial (or Hatchers Delta-) complexes and homology
(Hatcher Section 2.1 and Appendix).
I will be lecturing on this project
in class and attendance is
optional. Also, students doing this project will
continue to do in-class presentations as before, and there will be some homework exercises.
2) Another topic of your choice from the several topics mentioned in the classnotes in passing, e.g. Brouwer's “invariance of domain" theorem in Rn, or that an open set in the plane is simply connected if and only if it is connected and its complement in the extended plane,
or higher homotopy groups, the triangulation of surfaces, the classification of compact connected bordered orientable surfaces, etc.
3)
Another topic of your choice, perhaps related
to your PhD topic (but talk to me about it first).
Or covering spaces of topological or Lie groups, etc. Please ask if you have any questions...
4) I may add some more things here later...
Please tell me by March 15 which project you are doing if you do not do the default project: ADDED: Since nobody indicated by the deadline that they would be doing a project, this option is no longer available as originally
offered.