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Rigidity and gluing for Morse and Novikov complexes

Octav CorneaAndrew Ranicki — 2003

Journal of the European Mathematical Society

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....

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