Department of Mathematical Sciences, Ritsumeikan University Web Page

Geometry Seminar

Speaker: Gaël Meigniez (Université de Bretagne-Sud)
Title: h-principles and foliations
Date: 16:30-18:00, Friday 24 July
Place: Biwako-Kusatsu Campus, West-Wing 7th Floor, the 1st Laboratory of Mathematics
Abstract:(collaboration with Francois Laudenbach)
Gromov’s h-principle is a collection of powerful tools to build geometric objects, by deformation of a formal data whose existence is easy to decide. This talk will introduce a new approach to the h-principle, in two steps. From the formal data, the first step builds a Haefliger Gamma-structure (singular foliation) of codimension zero with the desired transverse geometry. This step works, for several interesting geometries, on all manifolds, even closed (I shall treat the example of contact geometry). The second step regularizes the Gamma-structure; it consists essentially in a simple adaptation of Thurston’s inflation method; it works for all geometries, but only on open manifolds. We use a special subdivision of the simplex, due to Thom.