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arXiv · 1709.04235

Topological quantum field theory for dormant opers

Yasuhiro Wakabayashi
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Abstract

The purpose of the present paper is to develop the enumerative geometry of dormant $G$-opers for a semisimple algebraic group $G$. In the present paper, we construct a compact moduli stack admitting a perfect obstruction theory by introducing the notion of a dormant faithful twisted $G$-oper (or a "$G$-do'per", for short). The resulting virtual fundamental class induces a semisimple $2$d TQFT (= $2$-dimensional topological quantum field theory) counting the number of $G$-do'pers. This $2$d TQFT gives an analogue of the Witten-Kontsevich theorem describing the intersection numbers of psi classes on the moduli stack of $G$-do'pers.

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Yasuhiro Wakabayashi. 2017-09-13. Topological quantum field theory for dormant opers. https://arxiv.org/abs/1709.04235

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