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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.06197 |
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| _version_ | 1866910996994457600 |
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| author | Pomerleano, Daniel Teleman, Constantin |
| author_facet | Pomerleano, Daniel Teleman, Constantin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral Kirwan Surjectivity Pomerleano, Daniel Teleman, Constantin Symplectic Geometry 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. |
| title | Integral Kirwan Surjectivity |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2410.06197 |