Corpus ID: 235898990

Projections in moduli spaces of Kleinian groups

  title={Projections in moduli spaces of Kleinian groups},
  author={Hala Alaqad and Jianhua Gong and Gaven J. Martin},
A two-generator Kleinian group 〈f, g〉 can be naturally associated with a discrete group 〈f, φ〉 with the generator φ of order 2 and where 〈f, φfφ〉 = 〈f, gfg〉 ⊂ 〈f, g〉, [〈f, gfg〉 : 〈f, φ〉] = 2 This is useful in studying the geometry of Kleinian groups since 〈f, g〉 will be discrete only if 〈f, φ〉 is, and the moduli space of groups 〈f, φ〉 is one complex dimension less. This gives a necessary condition in a simpler space to determine the discreteness of 〈f, g〉. The dimension reduction here is… Expand

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