The aim of this paper is to make progress in the understanding of the Scherk– Schwarz dimensional reduction in terms of a compactification in the presence of background fluxes and torsion. From the eleven dimensional supergravity point of view, we find that a general E6(6) S-S phase may be obtained by turning on an appropriate background torsion, together with suitable fluxes, some of which can...

In 1937, Baer solved the classification problem for the torsion-free abelian groups of rank 1. Since then, despite the efforts of many mathematicians, no satisfactory solution has been found of the classification problem for the torsion-free abelian groups of rank n ≥ 2. So it is natural to ask whether the classification problem for the higher rank groups is genuinely difficult. In this article...

We show that three-dimensional N=8 Sp(N) and SO(2N + 1) gauge theories flow to the same strong coupling fixed point. As a consequence, the corresponding orientifold two-planes in type IIA string theory are described at strong coupling and low-energies by the same M theory background. In the large N limit, these assertions are confirmed by studying discrete torsion in the supergravity theory cor...

Let M be a compact oriented simply-connected manifold of dimension at least 8. Assume M is equipped with a torsion-free semi-free circle action with isolated fixed points. We prove M has a perfect invariant Morse-Smale function. The major ingredient in the proof is a new cancellation theorem for the invariant Morse theory.

Let M be a closed COO -manifold of dimension n. Both R-torsion and analytic torsion are smooth invariants of acyclic orthogonal (or unitary) representations P of the fundamental group 1f l (M). The Reidemeister-Franz torsion (or R-torsion) r M(P) of P is defined in terms of the combinatorial structure of M given by its smooth triangulations. The analytic torsion T M(P) was introduced by Ray and...

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically, let G be a compact connected Lie group with no torsion in its fundamental group, let T be a maximal torus of G, and let M be a compact Hamiltonian G-space. Let...