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A type of non-equivalent pseudogroups. Application to foliations

Jesús A. Alvarez López (1992)

Annales Polonici Mathematici

A topological result for non-Hausdorff spaces is proved and used to obtain a non-equivalence theorem for pseudogroups of local transformations. This theorem is applied to the holonomy pseudogroup of foliations.

A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds

Stefan Friedl, Stefano Vidussi (2013)

Journal of the European Mathematical Society

In this paper we show that given any 3-manifold N and any non-fibered class in H 1 ( N ; Z ) there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.

A weak regularity theorem for real analytic optimal control problems.

Hector J. Sussmann (1986)

Revista Matemática Iberoamericana

We consider real analytic finite-dimensional control problems with a scalar input that enters linearly in the evolution equations. We prove that, whenever it is possible to steer a state x to another state y by means of a measurable control, then it is possible to steer x to y by means of a control that has an extra regularity property, namely, that of being analytic on an open dense subset of its interval of definition. Since open dense sets can have very small measure, this is a very weak property....

Adams spectral sequence and higher torsion in MSp*.

Boris I. Botvinnik, Stanley O. Kochman (1996)

Publicacions Matemàtiques

In this paper we study higher torsion in the symplectic cobordism ring. We use Toda brackets and manifolds with singularities to construct elements of higher torsion and use the Adams spectral sequence to determine an upper bound for the order of these elements.

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