Evans, JD;
(2014)
Quantum cohomology of twistor spaces and their Lagrangian submanifolds.
Journal of Differential Geometry
, 96
(3)
pp. 353-397.
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Abstract
We compute the classical and quantum cohomology rings of the twistor spaces of 6-dimensional hyperbolic manifolds and the eigenvalues of quantum multiplication by the first Chern class. Given a half-dimensional totally geodesic submanifold we associate, after Reznikov, a monotone Lagrangian submanifold of the twistor space. In the case of a 3-dimensional totally geodesic submanifold of a hyperbolic 6-manifold, we compute the obstruction term m0 in the Fukaya-Floer A∞-algebra of a Reznikov Lagrangian and calculate the Lagrangian quantum homology. There is a well-known correspondence between the possible values of m0 for a Lagrangian with nonvanishing Lagrangian quantum homology and eigenvalues for the action of c1 on quantum cohomology by quantum cup product. Reznikov’s Lagrangians account for most of these eigenvalues, but there are four exotic eigenvalues we cannot account for.
| Type: | Article |
|---|---|
| Title: | Quantum cohomology of twistor spaces and their Lagrangian submanifolds |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://projecteuclid.org/euclid.jdg/1395321845 |
| Language: | English |
| Additional information: | Copyright © 2014. First published in Journal of Differential Geometry 96:3 (2014), published by International Press. |
| 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 |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1360050 |
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