The $\mathbb{L}^ \bullet$-Homology fundamental class for singular spaces and the stratified Novikov conjecture
Also appears in collection : Analysis, geometry and topology of stratified spaces / Analyse, géométrie et topologie des espaces stratifiés
An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for those oriented singular spaces, which are integral intersection homology Poincaré spaces. Our approach constructs a morphism of ad theories from intersection Poincaré bordism to L-theory. We shall indicate an application to the stratified Novikov conjecture. The latter has been treated analytically by Albin, Leichtnam, Mazzeo and Piazza.
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