Geodesic
Rigidity and gluing for Morse and Novikov complexes
Journal of the European Mathematical Society, Tome 5 (2003) no. 4, pp. 343-394.

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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,ohgr) with c1|pgr2(M)=[ohgr]|pgr2(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 C0 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.
DOI : 10.1007/s10097-003-0052-6
Classification : 58-XX, 00-XX
Keywords: 
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     author = {Octav Cornea and Andrew Ranicki},
     title = {Rigidity and gluing for {Morse} and {Novikov} complexes},
     journal = {Journal of the European Mathematical Society},
     pages = {343--394},
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     doi = {10.1007/s10097-003-0052-6},
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Octav Cornea; Andrew Ranicki. Rigidity and gluing for Morse and Novikov complexes. Journal of the European Mathematical Society, Tome 5 (2003) no. 4, pp. 343-394. doi : 10.1007/s10097-003-0052-6. http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0052-6/

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