Edinburgh Research Archive
 Please use this identifier to cite or link to this item: http://hdl.handle.net/1842/240

 This item has been viewed 3 times in the last year. View Statistics

Files in This Item:

File Description SizeFormat
 Title: Rigidity and gluing for Morse and Novikov complexes Authors: Ranicki, AndrewCornea, Octav Issue Date: 12-May-2003 Citation: http://arxiv.org/pdf/math.AT/0107221 Publisher: Final version, accepted for publication by the Journal of the European Mathematical Society 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. URI: http://hdl.handle.net/1842/240 Appears in Collections: Mathematics publications