Gerard P. BARBANSON
WHITNEY REGULARITY OF THE IMAGE OF THE CHEVALLEY MAP.
(234K, .pdf)

ABSTRACT.  A closed set F is Whitney 1-regular if for all compact K in F, there exists a C>0 such that any two points x and x' in K can be joined by a path of length L less or equal to C|x-x'|. In this note we prove the Whitney regularity of the image of the Chevalley map defined by an integrity basis of the subalgebra of polynomials invariant by a finite orthogonal reflection group. The proof relies upon a Glaeser characterization of Whitney regular sets and a version of a Lojasiewicz extension theorem adjusted to r-regular jets of order m larger than r.