Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e duality, Hilbert complexes and geometric applications   Let $(M,g)$ an open and oriented riemannian manifold. The aim of this paper
is to study some properties of the two following sequences of $L^2$ cohomology
groups: $H^i_{2,m\rightarrow M}(M,g)$ defined as the image
$\im(H^i_{2,min}(M,g)\rightarrow H^i_{2,max}(M,g))$ and
$\bar{H}^i_{2,m\rightarrow M}(M,g)$ defined as
$\im(\bar{H}^i_{2,min}(M,g)\rightarrow \bar{H}^i_{2,max}(M,g))$. We show, under
certain hypothesis, that the first sequence is the cohomology of a suitable
Hilbert complex which contains the minimal one and is contained in the maximal
one. We also show that when the second sequence is finite dimensional then
Poincar\'e duality holds for it and that, in the same assumptions, when
$dim(M)\equiv0\ mod\ 4$ we can use it to define a $L^2$ signature on $M$.
Moreover we show several applications to the intersection cohomology of compact
smoothly stratified pseudomanifolds and we get some results about the
Friedrichs extension $\Delta_{i}^\mathcal{F}$ of $\Delta_{i}$.

8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc