Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Ray-Singer conjecture. I. A manifold with a smooth boundary   This paper is devoted to a proof of a generalized Ray-Singer conjecture for a
manifold with boundary (the Dirichlet and the Neumann boundary conditions are
independently given on each connected component of the boundary and the
transmission boundary condition is given on the interior boundary). The
Ray-Singer conjecture \cite{RS} claims that for a closed manifold the
combinatorial and the analytic torsion norms on the determinant of the
cohomology are equal. For a manifold with boundary the ratio between the
analytic torsion and the combinatorial torsion is computed. Some new general
properties of the Ray-Singer analytic torsion are found. The proof does~not use
any computation of eigenvalues and its asymptotic expansions or explicit
expressions for the analytic torsions of any special classes of manifolds.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph