On a conjecture of Rose

John P. Dalbec, Hal Schenck

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)151-154
Number of pages4
JournalJournal of Pure and Applied Algebra
Issue number2
StatePublished - Dec 7 2001
Externally publishedYes


  • 13C10
  • 13D40
  • 41A15
  • 52B20

ASJC Scopus subject areas

  • Algebra and Number Theory


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