Cohomology of Manifolds and Groups
Timings and Venue:
- Venue: LH-III (ground floor),
Department of Mathematics.
- Lecture times: Tue, Thu
& Fri, 11:00 a.m - 12:00 p.m. (Note: Friday will usually be
a zero hour).
- First Meeting: Thu, January 5,
2012, 11:00 a.m. (in LH-III).
- Tutorial/Quiz
times: to be
announced.
Course
Notes:
The course will be taught with
a virtual whiteboard (using a Tablet PC). The lectures
are posted
here in PDF as well as with AUDIO.
Note: The
whiteboard files are in Landscape
mode. Please ensure that the setting is in this
mode when printing and rotate while viewing.
Planned
topics:
The
goal of this course is to show how algebraic topology can be used to
answer geometric and group theoretic questions. Topics include:
- Whitehead's
theory of Cell-by-Cell constructions.
- Cohomology
of Groups.
- Obstruction
theory.
- Duality
theorems for manifolds.
Basic
knowledge of homology (but not cohomology) and manifolds is assumed.
Assignments:
The course assignments will be one of the
following (your choice). Choose relevant topics:
- Update Wikipedia pages.
- Build Haskell code.
- Formalise proofs in Isabelle/Isar
If you do not understand choice 2 & 3,
don't worry. These will be explained in the course (You can also choose
to stick to 1).
Organisation:
Communication for the course will be through a Google+
circle and the (experimental) wave at https://wavereactor.appspot.com/ besides
the course web page.
References:
Some
relevant references:
- Kenneth Brown, Cohomology of Groups.
- Ross Geoghegan: Topological methods in Group theory.
- Allen Hatcher: Algebraic Topology.
I also strongly recommend the beautiful book A course in simple-homotopy
theory by Cohen.
Lectures: