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. Moreover, a semisimple 2d TQFT (= 2-dimensional
topological quantum field theory) counting the number of G-do'pers is
obtained by means of the resulting virtual fundamental class. This 2d TQFT
gives an analogue of the Witten-Kontsevich theorem describing the intersection
numbers of psi classes on the moduli stack of G-do'pers.Comment: 64 pages, the title is changed, some mistakes are correcte