Talk:Gysin homomorphism

Latest comment: 4 years ago by Wundzer in topic Add construction with spectral sequences

Sphere bundle

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It surely needs to be mentioned that the sphere bundle in question should be oriented, unless one is using twisted or Z/2 coefficients. 31.205.108.80 (talk) 14:01, 14 June 2013 (UTC)Reply

Done. -- Taku (talk) 20:03, 19 July 2017 (UTC)Reply

Merge proposal

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On 05:49, 27 December 2014‎ User:TakuyaMurata proposed that Shriek map and this article Gysin sequence, be merged. He did not explain why. Below is space for a discussion.

  • I'd just like to cast a vote AGAINST merging the shriek map page with this one as they are quite distinct concepts. The Gysin sequence is more fundamental to topology while the shriek is more fundamental to algebraic geometry.Skeesix (talk) 15:16, 8 March 2015 (UTC)Reply

Add algebraic geometry section

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I have started writing up a section for defining the gysin morphism...

Algebraic Geometry

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The Gysin morphism

 

for a regular embedding   of codimension   where   are schemes of finite type over a field can be defined as follows: consider a dimension   subvariety  . From the pullback square

 

we can construct a bundle over  , the pullback of the normal bundle  , and a variety   embedding into this bundle. We define this variety as

 

where   is the ideal sheaf  . Since we have an isomorphism   we can take

I also had a draft on the definition of Fulton's refined Gysin homomorphism. I just have put it to the article. Maybe you want to expand/rewrite it with your materials. -- Taku (talk) 08:14, 18 July 2017 (UTC)Reply

Add Complex Geometry Sections

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Given a complex submanifold   there is a gysin morphism from the cohomology of   to the cohomology of  . This morphism is given by the top chern class of the normal bundle. This page should include this construction and give examples.

Add construction with spectral sequences

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The Gysin and Wang morphisms can be constructed using spectral sequences. Check out these *very informative* notes https://www.math.wisc.edu/~maxim/spseq.pdf — Preceding unsigned comment added by Wundzer (talkcontribs) 01:57, 11 February 2020 (UTC)Reply