SO(3)-invariant G₂-cobordisms

2020/01/05 by Chihara, Ryohei
#53C15 #53C26 #53C38 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/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 SL(3;ℂ)-structures on a 6-manifold via closed G₂-structures. Under SO(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.

Related

• Cobordism of G-manifolds
• Bordism and resolution of singularities
• The geometric cobordism hypothesis
• Some remarks on h-cobordisms between smooth 4-manifolds
• The intrinsic torsion of SU(3) and G₂ structures