Special Lagrangian cycles and Calabi-Yau transitions
Tristan C. Collins, Sergei Gukov, Sebastien Picard, Shing-Tung Yau
TL;DR
This paper constructs special Lagrangian 3-spheres in non-Kähler Calabi-Yau geometries arising from topological transitions, revealing a duality between holomorphic and special Lagrangian cycles during conifold transitions.
Contribution
It introduces a method to construct special Lagrangian 3-spheres in non-Kähler Calabi-Yau threefolds derived from conifold transitions.
Findings
Existence of special Lagrangian 3-spheres in Fu-Li-Yau geometries
Conifold transitions exchange holomorphic 2-cycles for special Lagrangian 3-cycles
Non-Kähler geometries can host special Lagrangian cycles related to Calabi-Yau transitions
Abstract
We construct special Lagrangian 3-spheres in non-K\"ahler compact threefolds equipped with the Fu-Li-Yau geometry. These non-K\"ahler geometries emerge from topological transitions of compact Calabi-Yau threefolds. From this point of view, a conifold transition exchanges holomorphic 2-cycles for special Lagrangian 3-cycles.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Black Holes and Theoretical Physics · Geometry and complex manifolds