The L-homology fundamental class for IP-spaces and the stratified Novikov conjecture - Banagl, Markus; Laures, Gerd; McClure, James E. (Selecta mathematica, 2019)
An IP-space is a pseudomanifold whose defining local properties imply that its middle perversity global intersection homology groups satisfy Poincaré duality integrally. We show that the symmetric signature induces a map of Quinn spectra from IP bordism to the symmetric L-spectrum of ZZ{\mathbb {Z}}, which is, up to weak equivalence, an E∞E∞E_∞ 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.
Gesehen am 22.08.2019