caa a22 4500 445843721 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00526-011-0391-1 doi (NATIONALLICENCE)springer-10.1007/s00526-011-0391-1 Merry Will Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, CB3 0WB, Cambridge, England aut On the Rabinowitz Floer homology of twisted cotangent bundles [Elektronische Daten] [Will Merry] Let (M, g) be a closed connected orientable Riemannian manifold of dimension n≥2. Let ω:=ω 0+π * σ denote a twisted symplectic form on T * M, where $${\sigma\in\Omega^{2}(M)}$$ is a closed 2-form and ω 0 is the canonical symplectic structure $${dp\wedge dq}$$ on T * M. Suppose that σ is weakly exact and its pullback to the universal cover $${\widetilde{M}}$$ admits a bounded primitive. Let $${H:T^{*}M\rightarrow\mathbb{R}}$$ be a Hamiltonian of the form $${(q,p)\mapsto\frac{1}{2}\left|p\right|^{2}+U(q)}$$ for $${U\in C^{\infty}(M,\mathbb{R})}$$. Let Σk:=H −1(k), and suppose that k>c(g, σ, U), where c(g, σ, U) denotes the Mañé critical value. In this paper we compute the Rabinowitz Floer homology of such hypersurfaces. Under the stronger condition that k>c 0(g, σ, U), where c 0(g, σ, U) denotes the strict Mañé critical value, Abbondandolo and Schwarz (J Topol Anal 1:307-405, 2009) recently computed the Rabinowitz Floer homology of such hypersurfaces, by means of a short exact sequence of chain complexes involving the Rabinowitz Floer chain complex and the Morse (co)chain complex associated to the free time action functional. We extend their results to the weaker case k>c(g, σ, U), thus covering cases where σ is not exact. As a consequence, we deduce that the hypersurface Σk is never (stably) displaceable for any k>c(g, σ, U). This removes the hypothesis of negative curvature in Cieliebak etal. (Geom Topol 14:1765-1870, 2010, Theorem 1.3) and thus answers a conjecture of Cieliebak, Frauenfelder and Paternain raised in Cieliebak etal. (2010). Moreover, following Albers and Frauenfelder (2009; J Topol Anal 2:77-98, 2010) we prove that for k>c(g, σ, U), any $${\psi\in\mbox{Ham}_{c}(T^{*}M,\omega)}$$ has a leaf-wise intersection point in Σk, and that if in addition $${\dim\, H_{*}(\Lambda M;\mathbb{Z}_{2})=\infty}$$, dim M≥2, and the metric g is chosen generically, then for a generic $${\psi\in\mbox{Ham}_{c}(T^{*}M,\omega)}$$ there exist infinitely many such leaf-wise intersection points. Springer-Verlag, 2011 Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 355-404 0944-2669 42:3-4<355 2011 42 526 https://doi.org/10.1007/s00526-011-0391-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-011-0391-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Merry Will Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, CB3 0WB, Cambridge, England aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 355-404 0944-2669 42:3-4<355 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer