The monoids l_{ 2q+1}(Z[\pi]) detect s-cobordisms amongst certain bordisms between stably diffeomorphic 2q-dimensional manifolds and generalise the Wall simple surgery obstruction groups, L_{ 2q+1}^s(Z[\pi]) \subset l_{ 2q+1}(Z[\pi]). In this paper we give exact sequences which completely describe l_{ 2q+1}(Z[\pi]) as a set and which we use to compute its Grothendieck group. As a consequence we deduce cancellation results for stably diffeomorphic manifolds with polycyclic-by-finite fundamental group.
Categories: math.GT