Strong Homotopy Structures from Foliations

Details Strong Homotopy Structures from Foliations Strong Homotopy Structures from Foliations

2012-04-11

arxiv.org/abs/1204.2467v1

Mathematics

Differential Geometry

25 pages

Scientific paper

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the space P of integral manifolds (of any dimension) of the characteristic distribution C of F. Similarly, characteristic cohomologies with local coefficients in the normal bundle TM/C of F may be interpreted as vector fields on P. In particular, they possess a (graded) Lie-bracket. In this paper, I show that such Lie-bracket comes from a strong homotopy structure at the level of cochains.

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