Cech Cohomology

[zheng xudong]

Dear seniors,

This is Xudong. Have you got some interesting materials on Cech
cohomology? I would like to give a short talk related to it as a
course project. One thing I am thinking is the relation with sheaf
cohomology. Considering fibre bundles over a good topological space
with fibre $F$ and structure group $G$, since the bundle is totally
determined by the transition functions, and cohomological transition
functions give isomorphic bundles, so the iso class of bundles is
given by the first Cech cohomology group. So I am looking for some
topological examples etc.

Thanks a lot.

[Yi Zhu]

Hi, Xudong,

In my experience, all cech stuff finally goes into the spectral sequence. To give more concrete examples in topology, Bott-Tu is the only resouce in my mind, e.g. to prove all cohomology theory coincide (singular, cech, de Rham), the defintion of euler class... To give more concrete examples in algebraic geometry, the basic example is the relation between Dolbeault cohomology and de Rham cohomology. Or compute the genus of P^1, elliptic curve by Cech. Or different interpretations of chern class of line bundles. Or Lefschetz (1,1) theorem. Most of these can be found in Griffiths-Harris.

Best,

Yi

--
You received this message because you are subscribed to the Google Groups "Prof. Shiu-chun Wong's Cocktail Seminar" group.
To post to this group, send email to cocktai...@googlegroups.com.
To unsubscribe from this group, send email to cocktailsemin...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/cocktailseminar?hl=en.