The Weinstein conjecture with multiplicities on spherizations
Author(s)
Heistercamp, Muriel
Editor(s)
Bourgeois, F.
Gutt, S.
Abbondandolo, A.
Bertelson, M.
Date issued
2011
Subjects
géométrie symplectique dynamique hamiltonienne fibrés
cotangents homologie de Floer flot de Reeb orbites périodiques homologie
Morse–Bott symplectic geometry Hamiltonian dynamic cotangent bundles Floer homology Reeb flow periodic orbits Morse–Bott homology
Abstract
Let <i>M</i> be a smooth closed manifold and <i>T∗M</i> its cotangent bundle endowed with the usual symplectic structure <i>ω = dλ</i>, where <i>λ</i> is the Liouville form. A hypersurface Σ ⊂ <i>T∗M</i> is said to be <i>fiberwise starshaped</i> if for each point <i>q</i> ∈ <i>M</i> the intersection Σ <i><sub>q</sub></i> := Σ∩<i>T∗<sub>q</sub>M</i> of Σ with the fiber at <i>q</i> is the smooth boundary of a domain in <i>T∗M</i> which is starshaped with respect to the origin 0<i><sub>q</sub></i> ∈ <i>T∗<sub>q</sub>M</i>. <br><br> In this thesis we give lower bounds on the growth rate of the number of closed Reeb orbits on a <i>fiberwise starshaped hypersurface</i> in terms of the topology of the free loop space of <i>M</i>. We distinguish the two cases that the fundamental group of the base space <i>M</i> has an exponential growth of conjugacy classes or not. If the base space <i>M</i> is simply connected we generalize the theorem of Ballmann and Ziller on the growth of closed geodesics to Reeb flows.
Notes
Thèse de doctorat : Université de Neuchâtel, 2011
Publication type
doctoral thesis
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