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Unfaithful complex hyperbolic triangle groups I: Involutions

Parker, John R.

Unfaithful complex hyperbolic triangle groups I: Involutions Thumbnail


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Abstract

A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the product of all three involutions are all nonloxodromic. We classify all such groups that are discrete.

Citation

Parker, J. R. (2008). Unfaithful complex hyperbolic triangle groups I: Involutions. Pacific Journal of Mathematics, 238(1), 145-169. https://doi.org/10.2140/pjm.2008.238.145

Journal Article Type Article
Publication Date Nov 1, 2008
Deposit Date Oct 29, 2009
Publicly Available Date Dec 1, 2017
Journal Pacific Journal of Mathematics
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 238
Issue 1
Pages 145-169
DOI https://doi.org/10.2140/pjm.2008.238.145
Keywords Complex hyperbolic geometry, Triangle group.
Publisher URL http://pjm.berkeley.edu/pjm/2008/238-1/p08.xhtml

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