Quasiconvex Subgroups and Nets in Hyperbolic Groups

cone type;finite automata;hyperbolic geometry;nets;quasiconvex;quasiconvexity;section

Mack, Thomas Patrick ; Calegari, Danny C.

University:California Institute of Technology

Department:Physics, Mathematics and Astronomy

关键词: cone type;    finite automata;    hyperbolic geometry;    nets;    quasiconvex;    quasiconvexity;    section;   

Others  :  https://thesis.library.caltech.edu/2461/1/thesis.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

Consider a hyperbolic group G and a quasiconvex subgroup H of G with [G:H] infinite. We construct a set-theoretic section s:G/H -> G of the quotient map (of sets) G -> G/H such that s(G/H) is a net in G; that is, any element of G is a bounded distance from s(G/H).This set arises naturally as a set of points minimizing word-length in each fixed coset gH.The left action of G on G/H induces an action on s(G/H), which we use to prove that H contains no infinite subgroups normal in G.