Vol. 310, No. 1, 2021

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Symplectic, Poisson, and contact geometry on scattering manifolds

Melinda Lanius

Vol. 310 (2021), No. 1, 213–256
Abstract

We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplectic setting. In particular, we construct scattering-symplectic spheres and scattering symplectic gluings between strong convex symplectic fillings of a contact manifold. By giving an explicit computation of the Poisson cohomology of a scattering symplectic manifold, we also introduce a new method of computing Poisson cohomology.

Keywords
b-symplectic, scattering, contact hypersurface, minimally degenerate Poisson
Mathematical Subject Classification 2010
Primary: 53D05
Secondary: 53D10, 53D17
Milestones
Received: 25 June 2019
Revised: 31 August 2020
Accepted: 1 October 2020
Published: 26 January 2021
Authors
Melinda Lanius
Department of Mathematics
University of Arizona
Tucson, AZ
United States