Communications in Analysis and Geometry

Volume 25 (2017)

Number 4

$G_2$–instantons, associative submanifolds and Fueter sections

Pages: 847 – 893



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


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.

Received 15 January 2013

Published 1 November 2017