dc.contributor.author Ranicki, Andrew dc.contributor.author Cornea, Octav dc.coverage.spatial 46 en dc.date.accessioned 2003-11-17T17:19:54Z dc.date.available 2003-11-17T17:19:54Z dc.date.issued 2003-05-12 dc.identifier.citation http://arxiv.org/pdf/math.AT/0107221 en dc.identifier.uri http://hdl.handle.net/1842/240 dc.description.abstract 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. en dc.format.extent 554684 bytes dc.format.mimetype application/pdf dc.language.iso en dc.publisher Final version, accepted for publication by the Journal of the European Mathematical Society en dc.title Rigidity and gluing for Morse and Novikov complexes en dc.type Preprint en
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