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.
@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},
publisher = {mathdoc},
volume = {5},
number = {4},
year = {2003},
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 PB - mathdoc 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 %I mathdoc %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
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