Topological field theory on r-spin surfaces and the Arf invariant
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866929389074120704 |
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| author | Runkel, Ingo Szegedy, Lóránt |
| author_facet | Runkel, Ingo Szegedy, Lóránt |
| contents | We give a combinatorial model for r-spin surfaces with parametrised boundary based on Novak (2015). The r-spin structure is encoded in terms of $\mathbb{Z}_r$-valued indices assigned to the edges of a polygonal decomposition. This combinatorial model is designed for our state sum construction of two-dimensional topological field theories on r-spin surfaces. We show that an example of such a topological field theory computes the Arf-invariant of an r-spin surface as introduced in Geiges, Gonzalo (2012) and Randal-Williams (2014). This implies in particular that the r-spin Arf-invariant is constant on orbits of the mapping class group, providing an alternative proof of that fact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_09978 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Topological field theory on r-spin surfaces and the Arf invariant Runkel, Ingo Szegedy, Lóránt Quantum Algebra High Energy Physics - Theory Mathematical Physics Geometric Topology We give a combinatorial model for r-spin surfaces with parametrised boundary based on Novak (2015). The r-spin structure is encoded in terms of $\mathbb{Z}_r$-valued indices assigned to the edges of a polygonal decomposition. This combinatorial model is designed for our state sum construction of two-dimensional topological field theories on r-spin surfaces. We show that an example of such a topological field theory computes the Arf-invariant of an r-spin surface as introduced in Geiges, Gonzalo (2012) and Randal-Williams (2014). This implies in particular that the r-spin Arf-invariant is constant on orbits of the mapping class group, providing an alternative proof of that fact. |
| title | Topological field theory on r-spin surfaces and the Arf invariant |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Geometric Topology |
| url | https://arxiv.org/abs/1802.09978 |