Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.10579 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909617104093184 |
|---|---|
| author | Miyazawa, Jin |
| author_facet | Miyazawa, Jin |
| contents | It is known that the Dirac index of a $Spin^c$ structure is localized to the characteristic submanifold. We introduce the notion of $G^{\pm}(n,s^+,s^-)$ structure on a manifold as a common generalization of the $Spin^c$ structure and the $H_n(s)$ structure defined by D.~Freed--M.~Hopkins, and formulate a version of characteristic submanifold for the $G^{\pm}(n,s^+,s^-)$ structure. We show that the $KO^*(pt)$-valued index associated with the $G^{\pm}(n,s^+,s^-)$ structure is localized to the characteristic submanifold. As an application, we give a topological sufficient condition for the moduli space of $Pin^-(2)$ monopoles to be orientable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_10579 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Localization of a $KO^{\ast}(\text{pt})$-valued index and the orientability of the $Pin^-(2)$ monopole moduli space Miyazawa, Jin Differential Geometry It is known that the Dirac index of a $Spin^c$ structure is localized to the characteristic submanifold. We introduce the notion of $G^{\pm}(n,s^+,s^-)$ structure on a manifold as a common generalization of the $Spin^c$ structure and the $H_n(s)$ structure defined by D.~Freed--M.~Hopkins, and formulate a version of characteristic submanifold for the $G^{\pm}(n,s^+,s^-)$ structure. We show that the $KO^*(pt)$-valued index associated with the $G^{\pm}(n,s^+,s^-)$ structure is localized to the characteristic submanifold. As an application, we give a topological sufficient condition for the moduli space of $Pin^-(2)$ monopoles to be orientable. |
| title | Localization of a $KO^{\ast}(\text{pt})$-valued index and the orientability of the $Pin^-(2)$ monopole moduli space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2109.10579 |