Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A topological classification of convex bodies   The shape of homogeneous, generic, smooth convex bodies as described by the
Euclidean distance with nondegenerate critical points, measured from the center
of mass represents a rather restricted class M_C of Morse-Smale functions on
S^2. Here we show that even M_C exhibits the complexity known for general
Morse-Smale functions on S^2 by exhausting all combinatorial possibilities:
every 2-colored quadrangulation of the sphere is isomorphic to a suitably
represented Morse-Smale complex associated with a function in M_C (and vice
versa). We prove our claim by an inductive algorithm, starting from the path
graph P_2 and generating convex bodies corresponding to quadrangulations with
increasing number of vertices by performing each combinatorially possible
vertex splitting by a convexity-preserving local manipulation of the surface.
Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist,
this algorithm not only proves our claim but also generalizes the known
classification scheme in [36]. Our expansion algorithm is essentially the dual
procedure to the algorithm presented by Edelsbrunner et al. in [21], producing
a hierarchy of increasingly coarse Morse-Smale complexes. We point out
applications to pebble shapes.

11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph