Geodesic
Rigidity and gluing for Morse and Novikov complexes
Journal of the European Mathematical Society, Tome 5 (2003) no. 4, pp. 343-394
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

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: 
@article{JEMS_2003_5_4_a1,
     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},
     year = {2003},
     volume = {5},
     number = {4},
     doi = {10.1007/s10097-003-0052-6},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0052-6/}
}
TY  - JOUR
AU  - Octav Cornea
AU  - Andrew Ranicki
TI  - Rigidity and gluing for Morse and Novikov complexes
JO  - Journal of the European Mathematical Society
PY  - 2003
SP  - 343
EP  - 394
VL  - 5
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0052-6/
DO  - 10.1007/s10097-003-0052-6
ID  - JEMS_2003_5_4_a1
ER  - 
%0 Journal Article
%A Octav Cornea
%A Andrew Ranicki
%T Rigidity and gluing for Morse and Novikov complexes
%J Journal of the European Mathematical Society
%D 2003
%P 343-394
%V 5
%N 4
%U http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0052-6/
%R 10.1007/s10097-003-0052-6
%F JEMS_2003_5_4_a1
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

Cité par Sources :