![[1241] Théorie de l’homotopie motivique et groupes d’homotopie stables, d’après Morel–Voevodsky, Isaksen–Wang–Xu, ...](/media/cache/video_light/uploads/video/Bourbaki.png)
publiée le 19 juin 2025
[1241] Théorie de l’homotopie motivique et groupes d’homotopie stables, d’après Morel–Voevodsky, Isaksen–Wang–Xu, ...
De Frédéric Déglise
The $\mathbb{L}^ \bullet$-Homology fundamental class for singular spaces and the stratified Novikov conjecture
Apparaît dans les collections : Analysis, geometry and topology of stratified spaces / Analyse, géométrie et topologie des espaces stratifiés, Exposés de recherche
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.
