A stable splitting of factorisation homology of generalised surfaces

For a manifold W and an Ed, the factorisation homology integral WA can be seen as a generalisation of the classical configuration space of labelled particles in W. It carries an action by the diffeomorphism group Diff partial derivative(W), and for the generalised surfaces Wg,1:=(#gSnxSn)\D2n, we have stabilisation maps among the quotients integral Wg,1A//Diff partial derivative(Wg,1) which increase the genus g. In the case where a highly-connected tangential structure theta is taken into account, this article describes the stable homology of these quotients in terms of the iterated bar construction B2nA and a tangential Thom spectrum MT theta, and addresses the question of homological stability.