# Rigidity and gluing for Morse and Novikov complexes

Journal of the European Mathematical Society (2003)

- Volume: 005, Issue: 4, page 343-394
- ISSN: 1435-9855

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topCornea, 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 -

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