The aim of this paper is to address the following question: given a contact manifold (Σ, ξ), what can be said about the aspherical symplectic manifolds (W,ω) bounded by (Σ, ξ) ? We first extend a theorem of Eliashberg, Floer and McDuff to prove that under suitable assumptions the map from H∗(Σ) to H∗(W ) induced by inclusion is surjective. We then apply this method in the case of contact manifo...

This paper proves the following conjecture of Boyer and Zhang: If a small hyperbolic knot in a homotopy sphere has a non-trivial cyclic surgery slope r, then it has an incompressible surface with non-integer boundary slope strictly between r − 1 and r + 1. I state this result below as Theorem 4.1, after giving the background needed to understand it. Corollary 1.1 of Theorem 4.1 is that any smal...

Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ, τ)-divergence. A (ρ, τ)-divergence generates a dually flat structure in the manifold of positive measures, as well as in the manifold of positive-definite matrices. The class is composed of decomposable ...

In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and Witten, we prove the following theorem: For any compact manifold with boundary and nonnegative scalar curvature, if it is spin and its boundary can be isometrically embedded into Euclidean space as a stric...

In [4J Orlik defined a free cyclic group action on a homotopy sphere constructed as a Brieskorn manifold and proved the following theorem: THEOREM. Every odd-dimensional homotopy sphere that bounds a para-llelizable manifold admits a free Zp-action for each prime p. On the other hand, it was shown ([3J) that there exists a free Zp-action on a 2n-1 dimensional homotopy sphere so that its orbit s...

Keywords: Neutral delayed differential equation Double Hopf bifurcation Normal form Multiple time scales Center manifold reduction a b s t r a c t In this paper, we study dynamics in a container crane model with delayed position feedback , with particular attention focused on non-resonant double Hopf bifurcation. By using multiple time scales and center manifold reduction methods, we obtain the...

Every compact smooth simply connected 3-manifold is a twisted 3-sphere, so every smooth simply connected 3-manifold is diffeomorphic to S.

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1) ; a robust example of such economies is provided . Theorem 2 establishes that the manifold fl of global pseudo-equilibria is a fiber bundle with the topological structure of a oneor two-fold covering space of G k . ", the space of k planes in R", where k is the number of assets in t...

Abstract The first part of this paper is a generalization the Feix–Kaledin theorem on existence hyperkähler metric neighborhood zero section cotangent bundle Kähler manifold. We show that problem constructing structure complex Lagrangian submanifold in holomorphic symplectic manifold reduces to certain deformations structures. recovered from twisted bundle. then every groupoid over compact Pois...