On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$

Abstract

We study Poincaré type $L^p$ inequality on a compact semialgebraic subset of ${\mathbb{R}}^n$ for $p>>1$. First we derive a local inequality by using a Lipschitz deformation retraction with estimates on its derivatives. Then, we extend the local inequality to a global inequality by employing double complex technique. As a consequence we obtain an isomorphism between $L^p$ cohomology and singular cohomology of a normal compact semialgebraic pseudomanifold.

36 pages