Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian spectral invariants, symplectic spinors and Frobenius
  structures I   This is the first of two articles aiming to introduce symplectic spinors into
the field of symplectic topology and the subject of Frobenius structures. After
exhibiting a (tentative) axiomating setting for Frobenius structures resp.
'Higgs pairs' in the context of symplectic spinors, we present immediate
observations concerning a local Schroedinger equation, the first structure
connection and the existence of 'spectrum', its topological interpretation and
its connection to 'formality' which are valid for the case of standard
Frobenius structures. We give a classification of the irreducibles and the
indecomposables of the latter in terms of certain $U(n)$-reductions of the
$G$-extension of the metaplectic frame bundle and a certain connection on it,
where $G$ is the semi-direct product of the metaplectic group and the
Heisenberg group, while the indecomposable case involves in addition the
combinatorial structure of the eigenstates of the $n$-dimensional harmonic
oscillator. In the second part, we associate an irreducible Frobenius structure
to any Hamiltonian diffeomorphism $\Phi$ on a cotangent bundle $T^*M$. The
spectral Lagrangian in $T^*(T^*M)$ associated to this Frobenius structure
intersects the zero-section $T^*M$ exactly at the fixed points of $\Phi$. We
give lower bounds for the number of fixed points of $\Phi$ by defining a
$C^*$-valued function on $T^*\tilde M$ defined by matrix coeficients of the
Heisenberg group acting on spinors, where $\tilde M$ is a certain
'complexification' of $M$, whose critical points are in bijection to the fixed
points of $\Phi$ resp. to the intersection of the spectral Lagrangian with the
zero section $T^*\tilde M$. We discuss how to define spectral invariants in the
sense of Viterbo and Oh by lifting the above function to a real-valued function
on an appropriate cyclic covering of $T^*\tilde M$ and using minimax-methods
for 'half-infinite' chains.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg