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Homotopy classes of rational functions. (Classes d’homotopie de fractions rationnelles.) (French) Zbl 1151.14016
Summary: Let \(k\) be a field of characteristic not 2 and \(n\geqslant \)1 be an integer; we show that the set of “algebraic” homotopy classes of rational functions of degree \(n\) with coefficients in \(k\) can be endowed with a graded monoid structure. Moreover, there is an isomorphism between this monoid and the monoid of orbits under the action of SL\(n(k)\) of non-degenerate symmetric bilinear forms on \(k^n\), endowed with the orthogonal sum.

14F35 Homotopy theory and fundamental groups in algebraic geometry
14A15 Schemes and morphisms
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