Topological field theory on r-spin surfaces and the Arf invariant

Autor:	Runkel, Ingo, Szegedy, Lóránt
Rok vydání:	2018
Předmět:	Mathematics - Quantum Algebra High Energy Physics - Theory Mathematical Physics Mathematics - Geometric Topology
Druh dokumentu:	Working Paper
DOI:	10.1063/5.0037826
Popis:	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. Comment: v2: 52 pages, removed classification of mapping class group orbits as suggested by referee, version to appear in Journal of Mathematical Physics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1802.09978 Zobrazit plný text záznamu View this record from Arxiv