A Lagrangian Piunikhin-Salamon-Schwarz morphism and two comparison homomorphisms in Floer homology

In this article we address two issues. First, we explore to what extent the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] an isomorphism between Hamiltonian Floer homology and the singular homology is established. In contrast, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian submanifold, in general. Depending on the minimal Maslov number, we construct for certain degrees two homomorphisms between Lagrangian Floer homology and singular homology. In degrees where both maps are defined we prove them to be isomorphisms. Examples show that this statement is sharp. Second, we construct two comparison homomorphisms between Lagrangian and Hamiltonian Floer homology. They underly no degree restrictions and are proven to be the natural analogs to the homomorphisms in singular homology induced by the inclusion map of the Lagrangian submanifold into the ambient symplectic manifold.Comment: 41 pages, 14 figures. v2: major revision, v3: included detailed transversality proofs. accepted by IMR

Translated points and Rabinowitz Floer homology

We prove that if a contact manifold admits an exact filling then every local contactomorphism isotopic to the identity admits a translated point in the interior of its support, in the sense of Sandon [San11b]. In addition we prove that if the Rabinowitz Floer homology of the filling is non-zero then every contactomorphism isotopic to the identity admits a translated point, and if the Rabinowitz Floer homology of the filling is infinite dimensional then every contactmorphism isotopic to the identity has either infinitely many translated points, or a translated point on a closed leaf. Moreover if the contact manifold has dimension greater than or equal to 3, the latter option generically doesn't happen. Finally, we prove that a generic contactomorphism on $\mathbb{R}^{2n+1}$ has infinitely many geometrically distinct iterated translated points all of which lie in the interior of its support.Comment: 13 pages, v2: numerous corrections, results unchange

A \Gamma-structure on Lagrangian Grassmannians

For n odd the Lagrangian Grassmannian of \R^{2n} is a \Gamma-manifold.Comment: 6 pages; v2: new coauthor, nicer proo

Quantitative analysis of single muscle fibre action potentials recorded at known distances

In vivo records of single fibre action potentials (SFAPs) have always been obtained at unknown distance from the active muscle fibre.\ud \ud A new experimental method has been developed enabling the derivation of the recording distance in animal experiments. A single fibre is stimulated with an intracellular micropipette electrode. The same electrode is used thereafter for labelling with an auto-fluorescent dye, Lucifer Yellow. In this method there is no use of chemical fixation. The tissue structure is kept as well as possible. In cross-sections the fluorescent fibre is seen and its position is quantitized with respect to the tip of one or more recording wire electrodes.\ud \ud Morphometric data, such as the recording distance and the fibre cross-sectional area, are used for the interpretation of parameters of the SFAPs (peak-peak amplitude, time between the first positive and negative peaks). The present results show that within 300 μm recording distance is not as dominant for the SFAP shape as expected.\ud \ud The method offers also a direct check of the relation between the muscle fibre; diameter and the conduction velocity of the action potential. In the present small set of data there is no simple linear relationship

The Weinstein conjecture in the presence of submanifolds having a Legendrian foliation

Helmut Hofer introduced in '93 a novel technique based on holomorphic curves to prove the Weinstein conjecture. Among the cases where these methods apply are all contact 3--manifolds $(M,\xi)$ with $\pi_2(M) \ne 0$. We modify Hofer's argument to prove the Weinstein conjecture for some examples of higher dimensional contact manifolds. In particular, we are able to show that the connected sum with a real projective space always has a closed contractible Reeb orbit.Comment: 11 pages, 2 figure

Flattening of the Phillips Curve and the Role of Oil Price: An Unobserved Components Model for the USA and Australia

We use the unobserved components model of Harvey (1989 and 2011) to estimate the Phillips curve (PC) for the USA and Australia, by augmenting it with oil prices. We found that the level coefficient of inflation and the coefficient of demand pressure have declined and contributed to the flattening of the Phillips curve. But the coefficient of oil prices has increased and has partly offset these effects. Therefore, oil prices are likely to play a significant role in future inflation rates.

The contact geometry of the restricted 3-body problem

We show that the planar circular restricted three body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the possibility of using the technology of Contact Topology to understand this particular dynamical system.Comment: 29 pages, 1 figur