On the structure of unoriented topological conformal field theories

We give a classification of open Klein topological conformal field theories in terms of Calabi-Yau $A_\infty$-categories endowed with an involution. Given an open Klein topological conformal field theory, there is a universal open-closed extension whose closed part is the involutive variant of the Hochschild chains of the open part.
Submitted for publication. Requested changes by the referee made. The report by the referee was generally positive and suggested changes were mainly on the level of exposition