an:05240795
Zbl 1151.14016
Cazanave, Christophe
Homotopy classes of rational functions
FR
C. R., Math., Acad. Sci. Paris 346, No. 3-4, 129-133 (2008).
00216388
2008
j
14F35 14A15
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.