Aarhus University Seal / Aarhus Universitets segl

Toric geometry of G2-manifolds

Research output: Working paper/Preprint Working paper

Standard

Toric geometry of G2-manifolds. / Madsen, Thomas Bruun; Swann, Andrew Francis.

arXiv.org, 2018.

Research output: Working paper/Preprint Working paper

Harvard

APA

CBE

Madsen TB, Swann AF. 2018. Toric geometry of G2-manifolds. arXiv.org.

MLA

Madsen, Thomas Bruun and Andrew Francis Swann Toric geometry of G2-manifolds. arXiv.org. 2018., 33 p.

Vancouver

Madsen TB, Swann AF. Toric geometry of G2-manifolds. arXiv.org. 2018 Mar 20.

Author

Madsen, Thomas Bruun ; Swann, Andrew Francis. / Toric geometry of G2-manifolds. arXiv.org, 2018.

Bibtex

@techreport{53266e9aa29c4dcbb8e88b48beb275a0,
title = "Toric geometry of G2-manifolds",
abstract = "We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz giving the geometry on an open dense set in terms a symmetric 3×3-matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to G2. We prove that the multi-moment maps exhibit the full orbit space topologically as a smooth four-manifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.",
author = "Madsen, {Thomas Bruun} and Swann, {Andrew Francis}",
year = "2018",
month = mar,
day = "20",
language = "English",
publisher = "arXiv.org",
type = "WorkingPaper",
institution = "arXiv.org",

}

RIS

TY - UNPB

T1 - Toric geometry of G2-manifolds

AU - Madsen, Thomas Bruun

AU - Swann, Andrew Francis

PY - 2018/3/20

Y1 - 2018/3/20

N2 - We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz giving the geometry on an open dense set in terms a symmetric 3×3-matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to G2. We prove that the multi-moment maps exhibit the full orbit space topologically as a smooth four-manifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.

AB - We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz giving the geometry on an open dense set in terms a symmetric 3×3-matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to G2. We prove that the multi-moment maps exhibit the full orbit space topologically as a smooth four-manifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.

M3 - Working paper

BT - Toric geometry of G2-manifolds

PB - arXiv.org

ER -