Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The spherical Plateau problem for group homology   Given a group homology class $h$ of a countable group $\Gamma$, we study a
corresponding homological Plateau problem inside a canonical classifying space
of $\Gamma$, which is defined using the regular representation of $\Gamma$ and
which is locally isometric to a Hilbert unit sphere. We investigate the
relation between group theoretic properties of the pair $(\Gamma,h)$ and the
geometry of its Plateau solutions. For instance, we prove that for a closed
oriented $3$-manifold $M$, the intrinsic geometry of any Plateau solution is
given by the hyperbolic part of $M$ endowed with one third of its hyperbolic
metric.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin