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Comments On a Discreteness Condition for Subgroups of SL(2, C)

Published online by Cambridge University Press:  20 November 2018

Troels Jørgensen
Troels Jørgensen*
Affiliation:
Harvard University, Cambridge, Massachusetts
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SL(2,C) is the group of all complex unimodular 2 × 2 matrices. A subgroup of SL(2, C) is said to be discrete if it does not contain any convergent sequence of distinct elements. A subgroup is said to be elementary if the commutator of any two elements of infinite order has trace 2. The discreteness condition which this note relates to is the following:

PROPOSITION 1. If two complex, unimodular 2 × 2 matrices X and Y generatea non-elementary, discrete group, then

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 87 - 92
Copyright
Copyright © Canadian Mathematical Society 1979

References

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