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Circle and Torus Actions in Exceptional Holonomy

Fowdar, Udhav; (2020) Circle and Torus Actions in Exceptional Holonomy. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The work in this thesis is an investigation of the geometric structures arising on S 1 and T 2 quotients of manifolds endowed with G2 and Spin(7)-structures. This was motivated by the work of Apostolov and Salamon who studied the circle reduction of G2 manifolds and showed that imposing that the quotient is Kähler leads to a rich geometry. We shall consider the following problems: 1. The S 1 quotient of Spin(7)-structures 2. The Kähler reduction of Spin(7) manifolds with T 2 actions 3. The S 1 -invariant G2 Laplacian flow 4. The SU(2) 2 ×U(1)-invariant G2 Laplacian flow on S 3 ×R 4 Our key results include expressions relating the intrinsic torsion of S 1 -invariant Spin(7)-structures to that of the quotient G2-structures, a new expression for the Ricci curvature of Spin(7)-structures only in terms of the intrinsic torsion, infinitely many new examples of (incomplete) Spin(7) metrics arising as T 2 bundles over Kähler manifolds with trivial canonical bundle, the first example of an inhomogeneous shrinking gradient G2 Laplacian soliton and a local classification of closed SU(2) 2 ×U(1)-invariant G2-structures on S 3 ×R 4 .

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Circle and Torus Actions in Exceptional Holonomy
Event: UCL (University College London)
Language: English
Additional information: Copyright © The Author 2020. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10109703
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