Equivariant Cerf theory and perturbative $SU(n)$ Casson invariants
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866908648578482176 |
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| author | Bai, Shaoyun Zhang, Boyu |
| author_facet | Bai, Shaoyun Zhang, Boyu |
| contents | We develop an equivariant Cerf theory for Morse functions on finite-dimensional manifolds with group actions, and adapt the technique to the infinite-dimensional setting to study the moduli space of perturbed flat $SU(n)$-connections. As a consequence, we prove the existence of perturbative $SU(n)$ Casson invariants on integer homology spheres for all $n\ge 3$, and write down an explicit formula when $n=4$. This generalizes the previous works of Boden and Herald. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_01118 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Equivariant Cerf theory and perturbative $SU(n)$ Casson invariants Bai, Shaoyun Zhang, Boyu Geometric Topology Differential Geometry We develop an equivariant Cerf theory for Morse functions on finite-dimensional manifolds with group actions, and adapt the technique to the infinite-dimensional setting to study the moduli space of perturbed flat $SU(n)$-connections. As a consequence, we prove the existence of perturbative $SU(n)$ Casson invariants on integer homology spheres for all $n\ge 3$, and write down an explicit formula when $n=4$. This generalizes the previous works of Boden and Herald. |
| title | Equivariant Cerf theory and perturbative $SU(n)$ Casson invariants |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2009.01118 |