Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant distributions and cohomology for geodesic flows and higher
  cohomology of higher-rank Anosov actions   We are motivated by a conjecture of A. and S. Katok to study the smooth
cohomologies of a family of Weyl chamber flows. The conjecture is a natural
generalization of the Livshitz Theorem to Anosov actions by higher-rank abelian
groups; it involves a description of top-degree cohomology and a vanishing
statement for lower degrees. Our main result, proved in Part II, verifies the
conjecture in lower degrees for our systems, and steps in the "correct"
direction in top degree. In Part I we study our "base case": geodesic flows of
finite-volume hyperbolic manifolds. We describe obstructions (invariant
distributions) to solving the coboundary equation in unitary representations of
the group of orientation-preserving isometries of hyperbolic N-space, and we
study Sobolev regularity of solutions. (One byproduct is a smooth Livshitz
Theorem for geodesic flows of hyperbolic manifolds with cusps.) Part I provides
the tools needed in Part II for the main theorem.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th