Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity and gluing for Morse and Novikov complexes   We obtain rigidity and gluing results for the Morse complex of a real-valued
Morse function as well as for the Novikov complex of a circle-valued Morse
function. A rigidity result is also proved for the Floer complex of a
hamiltonian defined on a closed symplectic manifold $(M,\omega)$ with
$c_{1}|_{\pi_{2}(M)}=[\omega]|_{\pi_{2}(M)}=0$. The rigidity results for these
complexes show that the complex of a fixed generic function/hamiltonian is a
retract of the Morse (respectively Novikov or Floer) complex of any other
sufficiently $C^{0}$ close generic function/hamiltonian. The gluing result is a
type of Mayer-Vietoris formula for the Morse complex. It is used to express
algebraically the Novikov complex up to isomorphism in terms of the Morse
complex of a fundamental domain. Morse cobordisms are used to compare various
Morse-type complexes without the need of bifurcation theory.

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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat