Abstract
We construct a two dimensional unoriented open/closed topological field theory from a finite graded group π:Gˆ↠{1,−1}, a π-twisted 2-cocycle θˆ on BGˆ and a character λ:Gˆ→U(1). The underlying oriented theory is a twisted Dijkgraaf–Witten theory. The construction is based on a detailed study of the (Gˆ,θˆ,λ)-twisted Real representation theory of kerπ. In particular, twisted Real representations are boundary conditions of the unoriented theory and the generalized Frobenius–Schur element is its crosscap state.
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