2017/10/20 by Ruben A. Hidalgo, Hidalgo, Ruben A.
Mathematics · #30F10 #30F40 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:30F10 #msc:30F40
paper · pdf · doi:10.48550/arxiv.1710.07520
Actualized. arXiv admin note: substantial text overlap with arXiv:1710.07518
arxiv created 2020/11/30 · arxiv updated 2022/02/27
An extended Kleinian group whose orientation-preserving half is a Schottky group is called an extended Schottky group. These groups correspond to the real points in the Schottky space. Their geometric structures is well known and it permits to provide information on the locus of fixed points of symmetries of handlebodies. A group generated by two different extended Schottky groups, both with the same orientation-preserving half, is called a dihedral extended Schottky group. We provide a structural description of these type of groups and, as a consequence, we obtain sharp upper bounds for the sum of the cardinalities of the connected components of the locus of fixed points of two or three different symmetries of a handlebody.