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arXiv · 2410.06197

Integral Kirwan Surjectivity

Daniel Pomerleano·Constantin Teleman
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Abstract

We refine Kirwan's surjectivity and formality theorems for a Hamiltonian G-action on a compact symplectic manifold M. For a regular value of the moment map, we show that the Kirwan map is surjective and additively split after inverting the orders of stabilizers in the reduction. In particular, for a free quotient, it is surjective integrally. We generalize this to a splitting of MU-module spectra. We also give a stable version of Kirwan's equivariant formality theorem. The novel idea is to exploit the Atiyah-Bott argument in Morava K-theory, then return to bordism and cohomology.

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Daniel Pomerleano, Constantin Teleman. 2024-10-08. Integral Kirwan Surjectivity. https://arxiv.org/abs/2410.06197

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