Rigidity and gluing for Morse and Novikov complexes

Cornea, Octav, and Ranicki, Andrew. "Rigidity and gluing for Morse and Novikov complexes." Journal of the European Mathematical Society 005.4 (2003): 343-394. <http://eudml.org/doc/277681>.

@article{Cornea2003,
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.},
author = {Cornea, Octav, Ranicki, Andrew},
journal = {Journal of the European Mathematical Society},
keywords = {Morse complex; Novikov complex; Floer complex; Hamiltonian; Morse complex; Novikov complex; Floer complex; Hamiltonian},
language = {eng},
number = {4},
pages = {343-394},
publisher = {European Mathematical Society Publishing House},
title = {Rigidity and gluing for Morse and Novikov complexes},
url = {http://eudml.org/doc/277681},
volume = {005},
year = {2003},
}

TY - JOUR
AU - Cornea, Octav
AU - Ranicki, Andrew
TI - Rigidity and gluing for Morse and Novikov complexes
JO - Journal of the European Mathematical Society
PY - 2003
PB - European Mathematical Society Publishing House
VL - 005
IS - 4
SP - 343
EP - 394
AB - 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.
LA - eng
KW - Morse complex; Novikov complex; Floer complex; Hamiltonian; Morse complex; Novikov complex; Floer complex; Hamiltonian
UR - http://eudml.org/doc/277681
ER -