43 research outputs found
On Diff(M)-pseudo-differential operators and the geometry of non linear grassmannians
We consider two principal bundles of embeddings with total space
with structure groups and where is the
groups of orientation preserving diffeomorphisms. The aim of this paper is to
describe the structure group of the tangent bundle of the two base manifolds:
From
the various properties described, an adequate group seems to be a group of
Fourier integral operators, which is carefully studied. This is the main goal
of this paper to analyze this group, which is a central extension of a group of
diffeomorphisms by a group of pseudo-differential operators which is slightly
different from the one developped in \cite{OMYK4}. We show that these groups
are regular, and develop the necessary properties for applications to the
geometry of A case of particular interest is where
connected components of are deeply linked with homotopy classes of
oriented knots. In this example, the structure group of the tangent space
is a subgroup of some group following the classical
notations of \cite{PS}. These constructions suggest some approaches in the
spirit of \cite{Ma2006} that could lead to knot invariants through a theory of
Chern-Weil forms