The Godbillon-Vey class, invariants of manifolds and linearised M-Theory

Details The Godbillon-Vey class, invariants of manifolds and linearised M-Theory The Godbillon-Vey class, invariants of manifolds and linearised M-Theory

2000-06-21

arxiv.org/abs/hep-th/0006169v4

Physics

High Energy Physics

High Energy Physics - Theory

50 pages, TeX, extended version

Scientific paper

We apply the Godbillon-Vey class to compute the transition amplitudes between some non-commutative solitons in M-Theory; our context is that of Connes-Douglas-Schwarz where they considered compactifications of matrix models on noncommutative tori. Two important consequences follow: we describe a new normalisation for the Abelian Chern-Simons theory using symplectic 4-manifolds as providing cobordisms for tight contact 3-manifolds and we construct a new(?) invariant for 3-manifolds. Moreover we modify the topological Lagrangian density suggested for M-Theory in a previous article to a \textsl{quadratic} one using the fact that the \emph{functor of immersions is a linearisation (or ``the differential'') of the functor of embeddings}

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