On a conjecture of Rose

[摘要] Let Delta be a triangulation of a topological n ball embedded in R-n. Rose has conjectured that if the module C-r(<()over cap>) of piecewise polynomial functions of smoothness r on <()over cap> is free, then so is Cr-1(<()over cap>). For n = 2, we prove the conjecture, and we show that it is false in all higher dimensions. (C) 2001 Published by Elsevier Science B.V.

[发布日期] 2001-12-07