Math 8306-07
List of Topics of Presentations
As you all know, each of you should make a topic presentation during
the school year. Below is a list of suggested topics. Sections refer
to Hatcher's textbook, unless a different source is mentioned. If you
find a source other than the one I suggest, you are welcome to use
it. The topics below have different length and level of
difficulty. Keep in mind, that you have to make a 50 minute
presentation, similar to a talk in a research seminar. You will have
to choose only the most important/interesting points of your topic at
your discretion and briefly sketch some proofs of main results or
ideas beyond them and place all this within 50 minutes.
Choose a topic and tell me, so that I will mark it unavailable and
discuss the date of your presentation with you. You may also choose a
topic not from this list - talk to me about that.
- Cohomology of SO(n) (Section 3.D) - Claimed by Eric for October
28
- The Gysin sequence and the cohomology of BSO(n) (Section 4.D, or
Husemoller or Milnor-Stasheff)
- Vector fields and the Euler characteristic (Milnor, Topology from
the Differentiable Viewpoint, Section 6; or any other source) -
Claimed by Jeongoo Cheh for January 24
- Poincare Duality (Section 3.3) Claimed by myself for October
30
- The Leray-Hirsch Theorem (Section 4.D) - Claimed by Sangwook
Kim for May 2
- Sheaf cohomology (Griffiths-Harris, Section 0.3) -Claimed by
Fei Xu for November 15
- The Eilenberg-Zilber Theorem (R. Switzer, Algebraic Topology...,
Chapter 13) - Claimed by myself for the Fall term
- The James construction and the homology of the loop space of a
suspension (Section 4.J) - Claimed by James for February 17
- Simplicial approximation (Section 2.C)
- Bott periodicity (Hatcher, Vector Bundles and K-Theory, Section
2.2, or May, Course in Algebraic Topology, Section 24.2)
- Currents and their cohomology (Griffiths-Harris, Section 3.2)
- The Lefschetz formula (Griffiths-Harris, Section 3.4)
- Cohomology of loop spaces (R. Cohen and J.D.S. Jones, A homotopy
theoretic realization of string topology; J.D.S. Jones, Cyclic
homology and equivariant homology, Invent. Math., 87 (1987),
403-423.) - Claimed by Kuerak for May 5
- Configuration spaces with summable labels and cohomology of free
loop spaces (D. Burghelea, The free loop space. I. Algebraic
topology. Algebraic topology (Evanston, IL, 1988), 59--85,
Contemp. Math., 96, Amer. Math. Soc., Providence, RI, 1989.)
- Cohomology of configuration spaces (original papers of Arnold,
Mat. Zam., and Fadell-Neuwirth, Math. Scand. 10 (1962) 111-118) -
Claimed by Javier for April 2
- The Adams spectral sequence (McCleary's Guide, Chapter 9)
- The Atiyah-Hirzebruch spectral sequence (McCleary's Guide, Section
11.3)
- Chern classes after Grothendieck (Hatcher, Vector Bunldes, Section
3.1)
- Curvature and characteristic classes (Appendix to
Milnor-Stasheff's book)
- The Atiyah-Singer Index Theorem (Section 5.4 of Luke-Mishchenko's
book)
- The Riemann-Roch Theorem (Section V.4 of M. Karoubi's book)
- Postnikov towers (Hatcher or J. P. May, A Concise Course in
Algebraic Topology) - Claimed by Jon for May 9
- Classifying spaces of posets and categories (Goerss and Jardine,
Simplicial homotopy theory) - Claimed by Muge for May 7
- De Rham cohomology with compact supports and relative de Rham
cohomology (Section V.4 of Karoubi, M.; Leruste, C. Algebraic topology
via differential geometry. London Mathematical Society Lecture Note
Series, 99. Cambridge University Press, Cambridge, 1987) - Claimed
by Hongjie Dong for April 28