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arXiv · 1409.0681

Syzygies in equivariant cohomology for non-abelian Lie groups

Matthias Franz
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Abstract

We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred sequence is exact if and only if the equivariant cohomology of X is reflexive, if and only if the equivariant Poincare pairing for X is perfect. Along the way we establish that the equivariant cohomology modules arising from the orbit filtration of X are Cohen-Macaulay. We allow singular spaces and introduce a Cartan model for their equivariant cohomology. We also develop a criterion for the finiteness of the number of infinitesimal orbit types of a G-manifold.

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Matthias Franz. 2014-09-02. Syzygies in equivariant cohomology for non-abelian Lie groups. https://doi.org/10.1007/978-3-319-31580-5_14

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