Poincar\xe9 duality for L^p cohomology on subanalytic singular spaces

Abstract

We investigate the problem of Poincaré duality for L^p differential forms on bounded subanalytic submanifolds of mathbb {R}^n (not necessarily compact). We show that, when p is sufficiently close to 1 then the L^p cohomology of such a submanifold is isomorphic to its singular homology. In the case where p is large, we show that L^p cohomology is dual to intersection homology. As a consequence, we can deduce that the L^p cohomology is Poincaré dual to L^q cohomology, if p and q are Hölder conjugate to each other and p is sufficiently large.