Internal circle uplifts, transversality and stratified G-structures

Abstract

We study stratied G-structures in N = 2 compactications of M-theory on eightmanifolds M using the uplift to the auxiliary nine-manifold ^M = M S1. We show that the cosmooth generalized distribution ^D on ^M which arises in this formalism may have pointwise transverse or non-transverse intersection with the pull-back of the tangent bundle of M, a fact which is responsible for the subtle relation between the spinor stabilizers arising on M and ^M and for the complicated stratied G-structure on M which we uncovered in previous work. We give a direct explanation of the latter in terms of the former and relate explicitly the dening forms of the SU(2) structure which exists on the generic locus U of M to the dening forms of the SU(3) structure which exists on an open subset ^ U of ^M , thus providing a dictionary between the eight- and nine-dimensional formalisms.