Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian perturbations in contact Floer homology   We study the contact Floer homology ${\rm HF}_*(W, h)$ introduced by
Merry-Uljarevi\'c, which associates a Floer-type homology theory to a Liouville
domain $W$ and a contact Hamiltonian $h$ on its boundary. The main results
investigate the behavior of ${\rm HF}_*(W, h)$ under the perturbations of the
input contact Hamiltonian $h$. In particular, we provide sufficient conditions
that guarantee ${\rm HF}_*(W, h)$ to be invariant under the perturbations. This
can be regarded as a contact geometry analogue of the continuation and
bifurcation maps along the Hamiltonian perturbations of Hamiltonian Floer
homology in symplectic geometry. As an application, we give an algebraic proof
of a rigidity result concerning the positive loops of contactomorphisms for a
wide class of contact manifolds.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int