Internal circle uplifts, transversality and stratified G-structures

الأصل · EN

We study stratified G-structures in N=2 compactifications of M-theory on eight-manifolds 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 stratified 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 defining forms of the SU(2) structure which exists on the generic locus U of M to the defining 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.