Communications in Analysis and Geometry

Volume 25 (2017)

Number 4

$G_2$–instantons, associative submanifolds and Fueter sections

Pages: 847 – 893

DOI: http://dx.doi.org/10.4310/CAG.2017.v25.n4.a4

Author

Thomas Walpuski (Department of Mathematics, Michigan State University, East Lansing, Michigan, U.S.A.)

Abstract

We give sufficient conditions for a family of $G_2$–instantons to be “spontaneously” be born out of a Fueter section of a bundle of moduli spaces of ASD instantons over an associative submanifold. This phenomenon is one of the key difficulties in defining the conjectural $G_2$ Casson invariant proposed by Donaldson and Thomas.

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Paper received on 15 January 2013.