Surgery and Excision for Furuta-Ohta invariants on Homology $S^1 \times S^3$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866911914604363776 |
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| author | Ma, Langte |
| author_facet | Ma, Langte |
| contents | We prove a surgery formula and an excision formula for the Furuta-Ohta invariant $λ_{FO}$ defined on homology $S^1 \times S^3$, which provides more evidence on its equivalence with the Casson-Seiberg-Witten invariant $λ_{SW}$. These formulae are applied to compute $λ_{FO}$ of certain families of manifolds obtained as mapping tori under diffeomorphisms of $3$-manifolds. In the course of the proof, we give a complete description of the degree-zero moduli space of ASD instantons on $4$-manifolds of homology $H_*(D^2 \times T^2; \mathbb{Z})$ with a cylindrical end modeled on $[0, \infty) \times T^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_04197 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Surgery and Excision for Furuta-Ohta invariants on Homology $S^1 \times S^3$ Ma, Langte Geometric Topology 57K41, 53C07 We prove a surgery formula and an excision formula for the Furuta-Ohta invariant $λ_{FO}$ defined on homology $S^1 \times S^3$, which provides more evidence on its equivalence with the Casson-Seiberg-Witten invariant $λ_{SW}$. These formulae are applied to compute $λ_{FO}$ of certain families of manifolds obtained as mapping tori under diffeomorphisms of $3$-manifolds. In the course of the proof, we give a complete description of the degree-zero moduli space of ASD instantons on $4$-manifolds of homology $H_*(D^2 \times T^2; \mathbb{Z})$ with a cylindrical end modeled on $[0, \infty) \times T^3$. |
| title | Surgery and Excision for Furuta-Ohta invariants on Homology $S^1 \times S^3$ |
| topic | Geometric Topology 57K41, 53C07 |
| url | https://arxiv.org/abs/2006.04197 |