$SO(3)$-invariant $G_2$-cobordisms

Ryohei Chihara

paper

$S O (3)$ -invariant $G_{2}$ -cobordisms

arXiv:2001.01200

Abstract

We study a bordism relation for stable 3-forms on a 6-manifold, which is a binary relation on the set of closed $S L (3; C)$ -structures on a 6-manifold via closed $G_{2}$ -structures. Under $S O (3)$ -symmetry and a co-associative condition the relation is reduced to a relation for geometric structures on a 3-manifold. Under these conditions we prove that the bordism relation is irreflexive and that the relation induces a more rigid one.

arXiv commentAccepted version

SO(3)-invariant G2​-cobordisms

Abstract

$S O (3)$ -invariant $G_{2}$ -cobordisms