Home > Research > Publications & Outputs > Exotic spheres and the topology of symplectomor...

Research

Associated organisational unit

Electronic data

  • 1407.3173

    Accepted author manuscript, 294 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

Keywords

View graph of relations

Exotic spheres and the topology of symplectomorphism groups

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Exotic spheres and the topology of symplectomorphism groups. / Dimitroglou Rizell, Georgios; Evans, Jonathan David.
In: Journal of Topology, Vol. 8, No. 2, 06.2015, p. 586-602.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dimitroglou Rizell, G & Evans, JD 2015, 'Exotic spheres and the topology of symplectomorphism groups', Journal of Topology, vol. 8, no. 2, pp. 586-602. https://doi.org/10.1112/jtopol/jtv007

APA

Dimitroglou Rizell, G., & Evans, J. D. (2015). Exotic spheres and the topology of symplectomorphism groups. Journal of Topology, 8(2), 586-602. https://doi.org/10.1112/jtopol/jtv007

Vancouver

Dimitroglou Rizell G, Evans JD. Exotic spheres and the topology of symplectomorphism groups. Journal of Topology. 2015 Jun;8(2):586-602. Epub 2015 May 29. doi: 10.1112/jtopol/jtv007

Author

Dimitroglou Rizell, Georgios ; Evans, Jonathan David. / Exotic spheres and the topology of symplectomorphism groups. In: Journal of Topology. 2015 ; Vol. 8, No. 2. pp. 586-602.

Bibtex

@article{d2baf9ff620a4190b827ce9c9e65027c,
title = "Exotic spheres and the topology of symplectomorphism groups",
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.",
keywords = "symplectic geometry, symplectomorphism group, exotic sphere, differential topology, gromoll filtration",
author = "{Dimitroglou Rizell}, Georgios and Evans, {Jonathan David}",
year = "2015",
month = jun,
doi = "10.1112/jtopol/jtv007",
language = "English",
volume = "8",
pages = "586--602",
journal = "Journal of Topology",
issn = "1753-8416",
publisher = "John Wiley and Sons Ltd",
number = "2",

}

RIS

TY - JOUR

T1 - Exotic spheres and the topology of symplectomorphism groups

AU - Dimitroglou Rizell, Georgios

AU - Evans, Jonathan David

PY - 2015/6

Y1 - 2015/6

N2 - 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.

AB - 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.

KW - symplectic geometry

KW - symplectomorphism group

KW - exotic sphere

KW - differential topology

KW - gromoll filtration

U2 - 10.1112/jtopol/jtv007

DO - 10.1112/jtopol/jtv007

M3 - Journal article

VL - 8

SP - 586

EP - 602

JO - Journal of Topology

JF - Journal of Topology

SN - 1753-8416

IS - 2

ER -