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G₂–instantons over twisted connected sums

Presented by: 
Thomas Walpuski Massachusetts Institute of Technology
Date: 
Tuesday 28th June 2016 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
In joint work with H. Sá Earp, I introduced a method to construct G₂–instantons over compact G₂–manifolds arising as the twisted connected sum of a matching pair of building blocks.  Using the fact that building blocks are K3 fibrations and work of Kuleshov on spherical bundles over K3s, this method can be used to produce concrete examples of G₂–instantons.  I will explain the abstract gluing theorem as well as one concrete example.  If time permits, I will also discuss the relation with work in progress (with A. Kovalev) on duality for building blocks, and/or the possibility of constructing singular G₂–instantons (with A. Jacob and H. Sá Earp).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons