RANDOM GROUPS CONTAIN SURFACE SUBGROUPS - JSTOR
Surfaces in Random Groups 6.4.1. A random k- generator group at any density D < 1/2 and length n contains a surface subgroup with probability 1 - 0(e~n ). In fact, it contains 0(en ) surfaces of genus 0(n). Moreover , these surfaces are quasiconvex. This state of affairs is summarized in Figure 1. A modification of the con- ................
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