Ranicki, Andrew

Cornea, Octav

46

2003-11-17T17:19:54Z

2003-11-17T17:19:54Z

2003-05-12

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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http://arxiv.org/pdf/math.AT/0107221

http://hdl.handle.net/1842/240

en

Final version, accepted for publication by the Journal of the European Mathematical Society

Rigidity and gluing for Morse and Novikov complexes

Preprint