Journal of Symplectic Geometry

Volume 14 (2016)

Number 1

Symplectormophism groups of non-compact manifolds, orbifold balls, and a space of Lagrangians

Pages: 203 – 226

DOI: https://dx.doi.org/10.4310/JSG.2016.v14.n1.a8

Authors

Richard Hind (Department of Mathematics, University of Notre Dame, Indiana, U.S.A.)

Martin Pinsonnault (Department of Mathematics, University of Western Ontario, London, On., Canada)

Weiwei Wu (Department of Mathematics, University of Georgia, Athens, Ga., U.S.A.)

Abstract

Let $M = L(n, 1)$ be a 3-dimensional Lens space. We show that there is a natural map from the loop space of the contact isometry group of M to the compactly supported symplectomorphism group of its symplectization $sM$ which induces a weak homotopy equivalence. We apply this result to determine the topology of a space of symplectic embeddings of orbifold balls and to show that the compactly supported sympectomorphism group of an orbifold ball is contractible. The result also applies to Lagrangian embeddings and we show that the space of Lagrangian $\mathbb{R}P^2$ in $T^* \mathbb{R}P^2$ is contractible.

Keywords

symplectic packing, symplectomorphism groups, space of Lagrangians, orbifold balls

2010 Mathematics Subject Classification

53D12, 53D35, 53Dxx

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Published 24 June 2016