By Y. Eliashberg
This publication provides the 1st steps of a idea of confoliations designed to hyperlink geometry and topology of three-d touch buildings with the geometry and topology of codimension-one foliations on third-dimensional manifolds. constructing virtually independently, those theories in the beginning look belonged to 2 diversified worlds: the idea of foliations is a part of topology and dynamical structures, whereas touch geometry is the odd-dimensional 'brother' of symplectic geometry. notwithstanding, either theories have constructed a few amazing similarities. Confoliations - which interpolate among touch constructions and codimension-one foliations - might be useful us to appreciate higher hyperlinks among the 2 theories. those hyperlinks supply instruments for transporting effects from one box to the other.It's positive aspects contain: a unified method of the topology of codimension-one foliations and call geometry; perception at the geometric nature of integrability; and, new effects, specifically at the perturbation of confoliations into touch constructions
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