EVENT DETAILS AND ABSTRACT

Title: Manifolds with G₂ holonomy: associative 3-folds and geometric transitions.
Speaker: Mark Haskins
Speaker Info: Imperial College, London
Brief Description:
Special Note:
Abstract:

Manifolds with holonomy G₂ are exotic cousins of Calabi-Yau 3-folds; they are very special Ricci-flat 7-manifolds of interest both to geometers and to String/M-theorists. Like Calabi-Yau 3-folds, G₂ manifolds admit interesting calibrated submanifolds: associative 3-folds and coassociative 4-folds. Examples of compact G₂ manifolds are hard to come by, particularly ones exhibiting interesting associative 3-folds. We construct many new compact G₂ manifolds containing rigid associative 3-folds. In many cases we determine the diffeomorphism type of the underlying 7-manifold and show that often the same 7-manifold can be given a holonomy G2 metric in a number of (apparently unrelated) ways; the number of associative 3-folds present in the construction varies accordingly. We show how many of our holonomy G₂ manifolds can be related to other holonomy G₂ manifolds via a G₂ analogue of the "reverse conifold transition".

The construction uses a combination of methods: algebraic geometry, complex Monge-Ampere equations on non-compact complex 3-folds and perturbation methods in geometric PDE.