The L-homology fundamental class for IP-spaces and the stratified Novikov conjecture

Abstract

An IP-space is a pseudomanifold whose defining local properties imply that its middle perversity global intersection homology groups satisfy Poincare duality integrally. We show that the symmetric signature induces a map of Quinn spectra from IP bordism to the symmetric L-spectrum of $${\mathbb {Z}}$$ , which is, up to weak equivalence, an $$E_\infty $$ ring map. Using this map, we construct a fundamental L-homology class for IP-spaces, and as a consequence we prove the stratified Novikov conjecture for IP-spaces whose fundamental group satisfies the Novikov conjecture.