On a conjecture of Rose

John P. Dalbec; Hal Schenck

doi:10.1016/S0022-4049(00)00175-4

On a conjecture of Rose

John P. Dalbec, Hal Schenck

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	151-154
Number of pages	4
Journal	Journal of Pure and Applied Algebra
Volume	165
Issue number	2
DOIs	https://doi.org/10.1016/S0022-4049(00)00175-4
State	Published - Dec 7 2001
Externally published	Yes

Keywords

13C10
13D40
41A15
52B20

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/S0022-4049(00)00175-4

Library availability

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abstract = "Let Δ be a triangulation of a topological n ball embedded in Rn. Rose has conjectured that if the module Cr({\^Δ}) of piecewise polynomial functions of smoothness r on {\^Δ} is free, then so is Cr-1({\^Δ}). For n=2, we prove the conjecture, and we show that it is false in all higher dimensions.",

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AB - 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.

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KW - 41A15

KW - 52B20

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On a conjecture of Rose

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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