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Ragini Singhal: Lectures

January 14, 2022
TITLE: Deformations of G2-instantons on nearly G2 manifolds

ABSTRACT: We will talk about the deformation theory of instantons on manifolds with a nearly parallel G2-structure. We formulate the deformation theory in terms of spinors and Dirac operators and prove that the space of infinitesimal deformations of an instanton is isomorphic to the kernel of an elliptic operator. Using this formulation we prove that abelian instantons are rigid. Then we apply our results to describe the deformation space of the characteristic connection on the four normal homogeneous nearly G2 manifolds. We also show that on three of these four spaces the deformations are genuine. 

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