Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse Theory for Geodesics in Conical Manifolds   The aim of this paper is to extend the Morse theory for geodesics to the
conical manifolds. We define these manifolds as submanifolds of $\R^n$ with a
finite number of conical singularities. To formulate a good Morse theory we
must use an appropriate definition of geodesic. The main theorem of this paper
claims that, although the energy is nonsmooth, we can find a continuous
retraction of its sublevels in absence of critical points. So, we can give a
good definition of index for isolated critical values and for isolated critical
points. We prove that Morse relations hold and, at last, we give a definition
of multiplicity of geodesics which is geometrical meaningful.

32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ