Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-contractible periodic trajectories of symplectic vector fields,
  Floer cohomology and symplectic torsion   For a closed symplectic manifold $(M,\omega)$, a compatible almost complex
structure $J$, a 1-periodic time dependent symplectic vector field $Z$ and a
homotopy class of closed curves $\gamma$ we define a Floer complex based on
1-periodic trajectories of $Z$ in the homotopy class $\gamma$. We suppose that
the closed 1-form $i_{Z_t}\omega$ represents a cohomology class
$\beta(Z):=\beta$, independent of $t$. We show how to associate to
$(M,\omega,\gamma,\beta)$ and to two pairs $(Z_i,J_i)$, $i=1,2$ with
$\beta(Z_i)=\beta$ an invariant, the relative symplectic torsion, which is an
element in the Whitehead group $Wh(\Lambda_0)$, of a Novikov ring $\Lambda_0$
associated with $(M,\omega,Z,\gamma)$. If the cohomology of the Floer complex
vanishes or if $\gamma$ is trivial we derive an invariant, the symplectic
torsion for any pair $(Z,J)$.
  We prove, that when $\beta(\gamma)\neq 0$, or when $\gamma$ is non-trivial
and $\beta$ is 'small', the cohomology of the Floer complex is trivial, but the
symplectic torsion can be non-trivial. Using the first fact we conclude results
about non-contractible 1-periodic trajectories of 1-periodic symplectic vector
fields. In this version we will only prove the statements for closed weakly
monotone manifolds, but note that they remain true as formulated for arbitrary
closed symplectic manifolds.

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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys