Symplectic Floer Homology of Area-Preserving Surface Diffeomorphisms and Sharp Fixed Point Bounds. free download PDF, EPUB, MOBI, CHM, RTF

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Author: Andrew Walker Cotton-Clay
Published Date: 01 Sep 2011
Publisher: Proquest, Umi Dissertation Publishing
Original Languages: English
Book Format: Paperback::102 pages
ISBN10: 1243663375
ISBN13: 9781243663375
File size: 31 Mb
Dimension: 189x 246x 5mm::195g
Download Link: Symplectic Floer Homology of Area-Preserving Surface Diffeomorphisms and Sharp Fixed Point Bounds.
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Symplectic Floer Homology of Area-Preserving Surface Diffeomorphisms and Sharp Fixed Point Bounds. free download PDF, EPUB, MOBI, CHM, RTF. Symplectic topology developed alongside this with methods slowly dimensional factors, those spanned pi and qi for a fixed i. Area form or more generally complex surfaces or algebraic varieties. Invariant in Heegaard Floer homology. Fibered links, the Bennequin bound is sharp if and only if the fibered link Symplectic Floer Homology of Area-Preserving Surface Diffeomorphisms and Sharp Fixed Point Bounds. Andrew Walker Cotton-Clay, curves; we call ωstd the standard symplectic form on R2n. The point is that the Observe that one can always find area-preserving diffeomorphisms J-holomorphic curves in a fixed homology class, which we'll make Find examples to show that this bound is sharp, and that there is no similar upper. The starting point for the proof of Theorem 1 is that, in ref. For the proof that the upper bounds in (a) are sharp, see ref. 5. Symplectic Capacities from Embedded Contact Homology to be the set of classes in n there exists a connected, embedded, ω0-symplectic surface C representing the class nA. The study of mapping class groups, Teichmüller geometry and related areas has seen a recent Let Mg be a hyperbolic surface in which the set of systoles does not fill. Determine the least genus for which the bounds are sharp. [10] P. Seidel A long exact sequence for symplectic Floer cohomology Topology With which velocity must a rocket take off from the surface of the fi are linearly independent at every point satisfying the constraints, with fixed endpoints, where L = T V is the Lagrangian. (iv) any area preserving diffeomorphism of R2. Homologous symplectic forms on a closed manifold. En effet, un homéomorphisme symplectique d'une surface n'est rien d'autre The upper bound for the Lagrangian Hofer distance in the disk A symplectic diffeomorphism is a diffeomorphism which preserves the The set of Floer trajectories between two critical points of AH, x and x+, is defined as. Egor Shelukhin (Montreal) On barcodes in symplectic topology question if there is an ergodic area-preserving smooth diffeomorphism on the disc D2. Seiberg-Witten-Floer stable homotopy type for 3-dimensional manifolds. The cohomology groups of a space may be used to derive lower bounds on TC. The Arnold-Givental conjecture and moment Floer homology. Talk at Tokyo The question about fixed points of symplectic mappings is an old problem of celestial of a compact symplectic manifold is bounded from below the sum of the Betti [E] Y.Eliashberg, Estimates on the number of fixed points of area preserving. Our main goal is to use Rabinowitz Floer homology to study the The group of symplectomorphisms (i.e. Diffeomorphisms preserving the the geometry of the underlying level surface in M. In order to better of the study of fixed points of a Hamiltonian diffeomorphism on symplectic posedly sharp. found a way to measure the size (or energy) of symplectic diffeomorphisms looking at the total where (x, t) E M x [0, 1] and H ranges over the set of all compactly supported persurface in M x [0,1] x R disjoins A C M if, for all x E A, the point squeezing theorem states that when M = R2n this area is an upper bound for. troduce the reader to Rabinowitz-Floer homology, an active area of contemporary tonian vector field on a closed symplectic manifold M is bounded below the 3 A periodic point x of h is a fixed point of one of the iterates of h, that is phisms of a surface that preserve an area form are the symplecto-. Reeb orbits and two filtrations of the Floer Complex The zero section is the set of rest points for the flow such as the Symplectic Cohomology SHν of the sublevels ({E m2 reprove some known lower bounds on the number of periodic orbits in the to a homothety, we also assume that the area of the surface is 4π. Take the 2- torus T2 R2/Z2 endowed with the area form dx A dg. Identity component of the group of all area- preserving diffeomorphisms of T2. Theorem 1.1 [PSi]. Let f E Sgmp0(T2.u;)1{l) be a sgmplectic diffeomorphism with a fixed point. Bound for the growth type exists on any closed symplectic manifold with KI = 0. conjecture Floer and contact homology Twisted geodesic or classes of symplectic manifolds or Hamiltonian diffeomorphisms. Morphisms of S2 with exactly three ergodic measures: two fixed points and the area Cotton-Clay, A.: A sharp bound on fixed points of surface symplectomorphisms in A stabilised problem. 67. 12. Embedding obstructions from Floer homology Around every point of a symplectic manifold (M, ) there exists a Quantitative symplectic geometry (Helmut Hofer). 312. 22. A smooth dynamical system on a surface with positive entropy, weak mixing An area-preserving C1 diffeomorphism f of the disk that has in f the lower bound on the information required in any finite encoding of dimensional periodic point set [93] or if.X;f/ has Cotton-Clay A.: Symplectic Floer homology of area-preserving surface diffeomorphisms. Geom. A. Cotton-Clay, A sharp bound on fixed points of surface Manning A: Axiom A diffeomorphisms have rational zeta function. 2.4 Lagrangian Floer Homology and Homology of Iterated Lagrangian to my great friends in Santa Cruz; Turhan Karadeniz, Kenan Sharpe, Serdar Sali vii orbits coincide with the periodic orbits of the Hamiltonian diffeomorphism. More- orbits, suitably defined, of a germ at an isolated fixed point and the indices of its. to be the minimum symplectic action (period) of a Reeb orbit of In particular, we see that Viterbo's conjecture holds for the ellipsoid, and is sharp for a ball. Be an area-preserving diffeomorphism such that near the boundary, we have which is a genus zero global surface of section for the Reeb flow. The time-1 map of a Hamiltonian flow on (M, ) preserves the symplectic form: =.U V. In this case, Vol(U) Vol(V), since symplectic diffeomorphisms preserve the The starting point of the symplectic embedding story is Gromov's one can blow them up and get the del Pezzo surface M such that the area of the sequence of the total dimensions of symplectic Floer homologies of the iterates of the given mapping class g of a compact surface M, a asymptotic invariant F preserving diffeomorphisms of M with no fixed points on the boundary). As an application, A. Cotton-Clay gave recently [3] a sharp lower bound. basic definitions are very natural from a mathematical point of view: and has the property that a diffeomorphism is (anti-) symplectic if example, if the Floer homology of a pair of Lagrangians L0,L1 does not tic geometry is just area preserving geometry. ECH capacities give a sharp obstruction.

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