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Zhaoting Wei's user avatar
Zhaoting Wei's user avatar
Zhaoting Wei's user avatar
Zhaoting Wei
  • Member for 12 years, 5 months
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Is there any "deep" relation between the localization theorem of equivariant cohomology and the localization theorem of equivariant K-theory
@Alexander Thank you for your comment! Yes I think Chern character map may be the answer and there are a lot of interesting theory on it (for example the paper by J. Block and E. Getzler "Equivariant cyclic homology and equivariant differential forms"). I will think more carefully about this.
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Reference Request: The Categorification of $\mathbb{Z}$ as cochain complexes of vector spaces
Thank you for your references! By details I mean how to define sum, difference, multiplication. I think $2$-term chain complexes is enough for sum and difference but may have difficulty to define mutiplications.
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Is there any "deep" relation between the localization theorem of equivariant cohomology and the localization theorem of equivariant K-theory
Thank you for your comments Damian! Yes, as far as I know the localization theorem is true essentially for compact abelian Lie groups.
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Does $G/H$ (quotient of a real semisimple Lie group by a Cartan subgroup) have a natural symplectic structure?
Yes it is very natural from the viewpoint of coadjoint orbits. Maybe I should think more carefully before asking this question. Nevertheless, thank you all!
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How to define the equivalence of Maurer-Cartan elements in an $L_{\infty}$-algebra?
Thank you very much! I will look at paper you suggested. By the way, since the equivalent class of Maurer-Cartan elements forms an $\infty$-groupoid, does it means that the "composition" of two equivalences is not unique?
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