Let Δ be a triangulation of a topological n ball embedded in Rn. Rose has conjectured that if the module Cr(Δ̂) of piecewise polynomial functions of smoothness r on Δ̂ is free, then so is Cr-1(Δ̂). For n=2, we prove the conjecture, and we show that it is false in all higher dimensions.
ASJC Scopus subject areas
- Algebra and Number Theory