1. CJM 2008 (vol 60 pp. 1336)
||Moving Frames for Lie Pseudo--Groups |
We propose a new, constructive theory of moving frames for Lie
pseudo-group actions on submanifolds. The moving frame provides an
effective means for determining complete systems of differential
invariants and invariant differential forms, classifying their
syzygies and recurrence relations, and solving equivalence and
symmetry problems arising in a broad range of applications.
Categories:58A15, 58A20, 58H05, 58J70
2. CJM 2007 (vol 59 pp. 712)
||Jet Modules |
In this paper we classify indecomposable modules for the Lie algebra
of vector fields on a torus that admit a compatible action of the algebra
of functions. An important family of such modules is given by spaces of jets
of tensor fields.
3. CJM 1999 (vol 51 pp. 585)
||Smooth Finite Dimensional Embeddings |
We give necessary and sufficient conditions for a norm-compact subset
of a Hilbert space to admit a $C^1$ embedding into a finite dimensional
Euclidean space. Using quasibundles, we prove a structure theorem
saying that the stratum of $n$-dimensional points is contained in an
$n$-dimensional $C^1$ submanifold of the ambient Hilbert space. This
work sharpens and extends earlier results of G.~Glaeser on paratingents.
As byproducts we obtain smoothing theorems for compact subsets of
Hilbert space and disjunction theorems for locally compact subsets
of Euclidean space.
Keywords:tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embedding