Exotic spheres and the topology of symplectomorphism groups

Dimitroglou Rizell, Georgios and Evans, Jonathan David (2015) Exotic spheres and the topology of symplectomorphism groups. Journal of Topology, 8 (2). pp. 586-602. ISSN 1753-8416

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Abstract

We show that, for certain families ϕs of diffeomorphisms of high‐dimensional spheres, the commutator of the Dehn twist along the zero‐section of T∗Sn with the family of pullbacks ϕ∗s gives a non‐contractible family of compactly supported symplectomorphisms. In particular, we find examples: where the Dehn twist along a parametrized Lagrangian sphere depends up to Hamiltonian isotopy on its parametrization; where the symplectomorphism group is not simply connected, and where the symplectomorphism group does not have the homotopy type of a finite CW complex. We show that these phenomena persist for Dehn twists along the standard matching spheres of the Am‐Milnor fibre. The non‐triviality is detected by considering the action of symplectomorphisms on the space of parametrized Lagrangian submanifolds. We find related examples of symplectic mapping classes for T∗(Sn×S1) and of an exotic symplectic structure on T∗(Sn×S1) standard at infinity.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Topology
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2608
Subjects:
ID Code:
132431
Deposited By:
Deposited On:
02 Apr 2019 09:20
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Dec 2020 06:52