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Topological quantum field theory for dormant opers
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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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Cited by 1 Pith paper
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Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$
For primes p ≤ 7 the count of dormant PGL_n-opers on any pointed curve is now explicit, because hypergeometric dormant opers are rigid and the lone exception at (7,3) is fixed by a conservation identity.
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