Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes
  from Group-Valued Moment Maps   We present a generalization of Minkowski's classic theorem on the
reconstruction of tetrahedra from algebraic data to homogeneously curved
spaces. Euclidean notions such as the normal vector to a face are replaced by
Levi-Civita holonomies around each of the tetrahedron's faces. This allows the
reconstruction of both spherical and hyperbolic tetrahedra within a unified
framework. A new type of hyperbolic simplex is introduced in order for all the
sectors encoded in the algebraic data to be covered. Generalizing the phase
space of shapes associated to flat tetrahedra leads to group valued moment maps
and quasi-Poisson spaces. These discrete geometries provide a natural arena for
considering the quantization of gravity including a cosmological constant. A
concrete realization of this is provided by the relation with the spin-network
states of loop quantum gravity. This work therefore provides a bottom-up
justification for the emergence of deformed gauge symmetries and quantum groups
in 3+1 dimensional covariant loop quantum gravity in the presence of a
cosmological constant.

28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn