Re: Digest for cocktailseminar@googlegroups.com - 2 Messages in 1 Topic

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Xudong Zheng

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Sep 4, 2010, 2:16:37 AM9/4/10

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Thanks a lot. To compare different cohomology is one of my thought.
The matter I am afraid is that it might become a totally homological
algebraic argument. I'd check Griffith and Harris for detail. I'd be
appreciate that.

best,

Xudong

On Sat, Sep 4, 2010 at 11:46 AM,
<cocktailsem...@googlegroups.com> wrote:
> Today's Topic Summary
>
> Group: http://groups.google.com/group/cocktailseminar/topics
>
> Cech Cohomology [2 Updates]
>
> Topic: Cech Cohomology
>
> zheng xudong <hacken...@gmail.com> Sep 02 09:02PM -0700 ^
>
> 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 <yz...@math.sunysb.edu> Sep 03 12:55AM -0400 ^
>
> 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
>
>
>
>
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