The space of geometric limits of abelian subgroups of PSL2(C)

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We give a local description of the topology of the space of all geometric limits of closed abelian subgroups of PSL2(C). More precisely, we give geometric descriptions for all possible neighborhoods of a point of this space. Intuition from hyperbolic geometry plays an important role by identifying PSL2(C) with the group of isometries of H-3. The tools and ideas developed in the authors' previous paper on one-generator closed subgroups of PSL2(R) allow one to reduce this problem to a problem about the geometric limits of certain closed subgroups of C and C*.
Publisher
HIROSHIMA UNIV, GRAD SCH SCI
Issue Date
2016-03
Language
English
Article Type
Article
Keywords

CLOSED SUBGROUPS

Citation

HIROSHIMA MATHEMATICAL JOURNAL, v.46, no.1, pp.1 - 36

ISSN
0018-2079
URI
http://hdl.handle.net/10203/221005
Appears in Collection
MA-Journal Papers(저널논문)
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