2013/07/08 by Ronen Peretz, Peretz, Ronen · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1307.1973
arxiv created 2014/11/10 · arxiv updated 2014/11/11
We consider the semigroup of étale polynomial mappings ℂ2→ℂ2 where the binary operation is composition. We prove that both the right and the left composition operators on this semigroup are injective. This is in contrast to the situation in the semigroup of the entire functions ℂ→ℂ which are locally injective, where the left composition operator is not injective. Our interest in the injectivity (of the left composition operator) results from a new approach to deal with the two dimensional Jacobian Conjecture. In this approach we construct a fractal like structure on the above (first) semigroup in order to use it to settle the conjecture (in preparation). Injectivity is crucial for that construction.