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September 2012 On the Thom-Boardman Symbols for Polynomial Multiplication Maps
Jiayuan Lin, Janice Wethington
Asian J. Math. 16(3): 367-386 (September 2012).

Abstract

The Thom-Boardman symbol was first introduced by Thom in 1956 to classify singularities of differentiable maps. It was later generalized by Boardman to a more general setting. Although the Thom-Boardman symbol is realized by a sequence of non-increasing, nonnegative integers, to compute those numbers is, in general, extremely difficult. In the case of polynomial multiplication maps, Robert Varley conjectured that computing the Thom-Boardman symbol for polynomial multiplication reduces to computing the successive quotients and remainders for the Euclidean algorithm applied to the degrees of the two polynomials. In this paper, we confirm Varley’s conjecture.

Citation

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Jiayuan Lin. Janice Wethington. "On the Thom-Boardman Symbols for Polynomial Multiplication Maps." Asian J. Math. 16 (3) 367 - 386, September 2012.

Information

Published: September 2012
First available in Project Euclid: 23 November 2012

zbMATH: 1268.58026
MathSciNet: MR2989225

Subjects:
Primary: 14J17 , 32S10 , 58K20 , 58K40

Keywords: polynomial multiplication maps , Thom-Boardman symbols , Toeplitz matrices

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 3 • September 2012
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