Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating the number of Reeb chords using a linear representation of
  the characteristic algebra   Given a chord-generic horizontally displaceable Legendrian submanifold
$\Lambda\subset P\times \mathbb R$ with the property that its characteristic
algebra admits a finite-dimensional matrix representation, we prove an
Arnold-type lower bound for the number of Reeb chords on $\Lambda$. This result
is a generalization of the results of Ekholm-Etnyre-Sullivan and
Ekholm-Etnyre-Sabloff which hold for Legendrian submanifolds whose
Chekanov-Eliashberg algebras admit augmentations. We also provide examples of
Legendrian submanifolds $\Lambda$ of $\mathbb C^{n}\times \mathbb R$, $n \ge
1$, whose characteristic algebras admit finite-dimensional matrix
representations, but whose Chekanov-Eliashberg algebras do not admit
augmentations. In addition, to show the limits of the method of proof for the
bound, we construct a Legendrian submanifold $\Lambda\subset \mathbb
C^{n}\times \mathbb R$ with the property that the characteristic algebra of
$\Lambda$ does not satisfy the rank property. Finally, in the case when a
Legendrian submanifold $\Lambda$ has a non-acyclic Chekanov-Eliashberg algebra,
using rather elementary algebraic techniques we obtain lower bounds for the
number of Reeb chords of $\Lambda$. These bounds are slightly better than the
number of Reeb chords that is possible to achieve with a Legendrian submanifold
whose Chekanov-Eliashberg algebra is acyclic.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph