2021/02/18 by Grigory Mikhalkin, Mikhalkin, Grigory, Mikhail Shkolnikov +1 · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2102.09324
openalex publication_date 2021/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The group of isometries of the hyperbolic 3-space is one of the simplest non-commutative complex Lie groups. Its quotient by the maximal compact subgroup naturally maps it back to the hyperbolic space. Each fiber of this map is diffeomorphic to the real projective 3-space. The resulting map can be viewed as the simplest non-commutative counterpart of the amoeba map introduced, in the commutative setting, by Gelfand, Kapranov and Zelevinsky. The paper surveys basic properties of the non-commutative amoebas and compares them against their commutative counterparts.