Title: G2-instantons over twisted connected sums
Speaker: Andriy Haydys, Bielefeld
Date: Thursday, August 28, 2014
Time: 09:00am-10:00am
Place: Seminar Room 313, Simons Center
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Abstract: The talk will be divided in two parts. First, I will construct G2-instantons over asymptotically cylindrical (ACyl) manifolds obtained from the building blocks of Corti-Haskins-Nordström-Pacini, using the familiar gradient flow method under a suitable boundary condition of ‘asymptotic stability’. I will provide nontrivial explicit examples produced with homological techniques.
Second, I will present a gluing theorem for such solutions compatible with the twisted connected sum construction, subject to an additional rigidity assumption on the limiting instantons ‘at infinity’. Time allowing, I will sketch some key elements of the proof, then discuss why it is difficult to obtain concrete examples using the same techniques as before and mention possible alternatives.