Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monoide des enlacements et facteurs orthogonaux (Monoids of linking
  pairings and orthogonal summands)   A linking pairing is a symetric bilinear pairing lambda: GxG --> Q/Z on a
finite abelian group. The set of isomorphism classes of linking pairings is a
non-cancellative monoid E under orthogonal sum, which is infinitely generated
and infinitely related. We propose a new presentation of E that enables one to
detect whether a linking pairing has a given orthogonal summand. The same
method extends to the monoid Q of quadratic forms on finite abelian groups. We
obtain a combinatorial classification of Q (that was previously known for
groups of period 4). As applications, we describe explicitly 3-manifolds having
a degree one map onto prescribed (or proscribed) lens spaces. Most of the
results extend to 3-manifolds endowed with a parallelization or a spin
structure. In particular, the Reidemeister--Turaev function detects the
existence of a spin preserving degree one map between a rational homology
3-sphere and a lens space.

9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph