LP COHOMOLOGY OF CONES AND HORNS

We prove the conjecture of J. Brasselet, M. Goresky, and R. MacPherson on the isomorphism between L(p) cohomology and intersection cohomology for a stratified space with a Riemannian metric and conical singularities. We prove the extension of this conjecture to spaces with f-horn singularities, where f(r) is any C(infinity) nondecreasing function. We study the L(p) Stokes property which states that the minimal closed extension of d acting on L(p) forms coincides with the maximal one. We prove that it implies the Borel-Moorse duality between the complexes of L(p) forms and L(q) forms. We also prove the converse for spaces with f-horn singularities under the condition that the integral integral-epsilon/0 f(R)-1 dr diverges.