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A classical proof that the algebraic homotopy class of a rational function is the residue pairing

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Type
Preprint
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arXiv ID: 1602.08129
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arXiv
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Abstract

C. Cazanave has identified the algebraic homotopy class of a rational function of 1 variable with an explicit nondegenerate symmetric bilinear form. Here we relate Cazanave's result to classical results and in particular identify Cazanave's form with a residue pairing from commutative algebra. We announce work identifying the local A1-degree of a polynomial map in several variables that has an isolated zero at the origin with the residue pairing.

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