Equivariant cohomology, syzygies and orbit structure
TLDR
In this paper, the Atiyah-Bredon sequence of equivariant cohomology modules arising from the filtration of X by orbit dimension was considered and it was shown that a front piece of this sequence is exact if and only if the H∗(BT )-module H ∗ T (X) is a certain syzygy.Abstract:
Let X be a “nice” space with an action of a torus T . We consider the Atiyah–Bredon sequence of equivariant cohomology modules arising from the filtration of X by orbit dimension. We show that a front piece of this sequence is exact if and only if the H∗(BT )-module H∗ T (X) is a certain syzygy. Moreover, we express the cohomology of that sequence as an Ext module involving a suitably defined equivariant homology of X. One consequence is that the GKM method for computing equivariant cohomology applies to a Poincare duality space if and only if the equivariant Poincare pairing is perfect.read more
Citations
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Journal ArticleDOI
Equivariant Hirzebruch class for singular varieties
TL;DR: In this paper, an equivariant version of the Hirzebruch class for singular varieties is developed for simplicial toric varieties, where the group acting is a torus and the localization theorem of Atiyah-Bott and Berline-Vergne is applied.
Journal ArticleDOI
Big polygon spaces
TL;DR: In this paper, a new class of compact orientable T manifolds, called big polygon spaces, were presented, which generalize a ''mutant'' constructed by Franz{Puppe [3] and are related to polygon space, which appear as their xed point sets.
Book ChapterDOI
Syzygies in Equivariant Cohomology for Non-abelian Lie Groups
TL;DR: In this article, the authors extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G.
Posted Content
Equivariant Hirzebruch class for singular varieties
TL;DR: In this paper, a relation of the properties of a singularity germ with its local Hirzebruch class is discussed, and the issue of positivity of coefficients in a certain expansion remains mysterious.
Journal ArticleDOI
A quotient criterion for syzygies in equivariant cohomology
TL;DR: In this paper, a necessary and sufficient criterion for the equivariant cohomology H * (BT) with real coefficients to be a certain syzygy as module over BT was provided.
References
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TL;DR: In this paper, the authors considered the action of a compact Lie group K on a space X and gave a description of equivariant homology and intersection homology in terms of Equivariant geometric cycles.
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