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We prove that the group $Aut_1(xi)$ of strict contactomorphisms, also known as quantomorphisms, of the standard tight contact structure $xi$ on $S^3$ is the total space of a fiber bundle $S^1 to Aut_1(xi) to SDiff(S^2)$ over the group of area-preserving $C^infty$-diffeomorphisms of $S^2$, and that it deformation retracts to its finite-dimensional sub-bundle $S^1 to U(2)cup cU(2) to O(3)$, where $U(2)$ is the unitary group and $c$ is complex conjugation.
We prove that that the homotopy type of the path connected component of the identity in the contactomorphism group is characterized by the homotopy type of the diffeomorphism group plus some data provided by the topology of the formal contactomorphis
Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $widetilde{N}^{11}=(Sp(2)times S^4)/S^3$, we construct a homogeneous isoparametric foliat
We consider convex contact spheres $Y$ all of whose Reeb orbits are closed. Any such $Y$ admits a stratification by the periods of closed Reeb orbits. We show that $Y$ resembles a contact ellipsoid: any stratum of $Y$ is an integral homology sphere,
Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting
Recently, there have been several breakthroughs in the classification of tight contact structures. We give an outline on how to exploit methods developed by Ko Honda and John Etnyre to obtain classification results for specific examples of small Seifert manifolds.