Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: O-minimal cohomology and definably compact definable groups   Let N be an o-minimal expansion of a real closed field. We develop cohomology
theory for the category of N-definable manifolds and N-definable maps, and use
this to solve the Peterzil-Steinhorn problem on the existence of torsion points
on N-definably compact N-definable abelian groups. We compute the cohomology
rings of N-definably compact N-definable groups, and we prove an o-minimal
analog of the Poincare duality theorem, the Alexander dualti theorem, the
Lefschetz duality theorem and the Lefschetz fixed point theorem.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int