6 papers
Cluster Homology
Octav Cornea, Francois Lalonde
We assign, to a Langrangian submanifold , a new homology which manages the bubbling of disks by means of auxiliary Morse data. This invariant of the Hamiltonian isotopy class of…
Homotopical dynamics in symplectic topology
J. -F. Barraud, O. Cornea
This is mainly a survey of recent work on algebraic ways to ``measure'' moduli spaces of connecting trajectories in Morse and Floer theories as well as related applications to symp…
Homotopical Dynamics IV: Hopf invariants and hamiltonian flows
Octavian Cornea
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact sett…
Rigidity and gluing for Morse and Novikov complexes
Octav Cornea, Andrew Ranicki
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…
Homotopical Dynamics: Suspension and Duality
Octavian Cornea
Flow type suspension and homotopy suspension agree for attractor-repellor homotopy data.The connection maps associated in Conley index theory to an attractor-repellor decomposition…
Homotopical Dynamics II: Hopf invariants, smoothings and the Morse complex
Octavian Cornea
The ambient framed bordism class of the connecting manifold of two consecutive critical points of a Morse-Smale function is estimated by means of a certain Hopf invariant. Applicat…