A stable splitting of factorisation homology of generalised surfaces

Abstract For a manifold and an ‐algebra , the factorisation homology can be seen as a generalisation of the classical configuration space of labelled particles in . It carries an action by the diffeomorphism group , and for the generalised surfaces , we have stabilisation maps among the quotients which increase the genus . In the case where a highly‐connected tangential structure is taken into account, this article describes the stable homology of these quotients in terms of the iterated bar construction and a tangential Thom spectrum , and addresses the question of homological stability.