Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e duality for $L^p$ cohomology on subanalytic singular spaces   We investigate the problem of Poincar\'e 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
Poincar\'e dual to $L^q$ cohomology, if $p$ and $q$ are H\"older conjugate to
each other and $p$ is sufficiently large.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys