Multi-moment maps

T. B. Madsen, A. Swann

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second and third Lie algebra Betti numbers are zero. We show that these form a special class of solvable Lie groups and provide a structural characterisation. We provide many examples of multi-moment maps for different geometries and use them to describe manifolds with holonomy contained in G(2) preserved by a two-torus symmetry in terms of tri-symplectic geometry of four-manifolds. (C) 2012 Elsevier Inc. All rights reserved.
OriginalsprogEngelsk
TidsskriftAdvances in Mathematics
Vol/bind229
Udgave nummer4
Sider (fra-til)2287-2309
Antal sider23
ISSN0001-8708
DOI
StatusUdgivet - 2012

Citer dette

Madsen, T. B., & Swann, A. (2012). Multi-moment maps. Advances in Mathematics, 229(4), 2287-2309. https://doi.org/10.1016/j.aim.2012.01.002
Madsen, T. B. ; Swann, A. / Multi-moment maps. I: Advances in Mathematics. 2012 ; Bind 229, Nr. 4. s. 2287-2309.
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Madsen, TB & Swann, A 2012, 'Multi-moment maps', Advances in Mathematics, bind 229, nr. 4, s. 2287-2309. https://doi.org/10.1016/j.aim.2012.01.002

Multi-moment maps. / Madsen, T. B.; Swann, A.

I: Advances in Mathematics, Bind 229, Nr. 4, 2012, s. 2287-2309.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Multi-moment maps

AU - Madsen, T. B.

AU - Swann, A.

PY - 2012

Y1 - 2012

N2 - We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second and third Lie algebra Betti numbers are zero. We show that these form a special class of solvable Lie groups and provide a structural characterisation. We provide many examples of multi-moment maps for different geometries and use them to describe manifolds with holonomy contained in G(2) preserved by a two-torus symmetry in terms of tri-symplectic geometry of four-manifolds. (C) 2012 Elsevier Inc. All rights reserved.

AB - We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second and third Lie algebra Betti numbers are zero. We show that these form a special class of solvable Lie groups and provide a structural characterisation. We provide many examples of multi-moment maps for different geometries and use them to describe manifolds with holonomy contained in G(2) preserved by a two-torus symmetry in terms of tri-symplectic geometry of four-manifolds. (C) 2012 Elsevier Inc. All rights reserved.

U2 - 10.1016/j.aim.2012.01.002

DO - 10.1016/j.aim.2012.01.002

M3 - Journal article

VL - 229

SP - 2287

EP - 2309

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

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ER -