Rigidity and gluing for Morse and Novikov complexes
| dc.creator | Cornea, Octav | |
| dc.creator | Ranicki, Andrew | |
| dc.date | 2001-07-30 | |
| dc.date | 2003-05-12 | |
| dc.date.accessioned | 2026-07-07T04:42:47Z | |
| dc.date.available | 2026-07-07T04:42:47Z | |
| dc.description | 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 $(M,ω)$ with $c_{1}|_{π_{2}(M)}=[ω]|_{π_{2}(M)}=0$. 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. | |
| dc.description | 46 pages, LATEX file with XYPIC diagrams, and one .EPS file. Final version, accepted for publication by the Journal of the European Mathematical Society | |
| dc.identifier | https://arxiv.org/abs/math/0107221 | |
| dc.identifier | http://arxiv.org/abs/math/0107221 | |
| dc.identifier | J. Eur. Math. Soc. 5, 343-394 (2003) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61934 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R70 | |
| dc.title | Rigidity and gluing for Morse and Novikov complexes | |
| dc.type | text |