Please use this identifier to cite or link to this item: https://doi.org/10.1353/ajm.2008.0010
Title: End invariants for SL(2,ℂ) characters of the one-holed torus
Authors: Tan, S.P. 
Wong, Y.L. 
Zhang, Y.
Issue Date: Apr-2008
Source: Tan, S.P., Wong, Y.L., Zhang, Y. (2008-04). End invariants for SL(2,ℂ) characters of the one-holed torus. American Journal of Mathematics 130 (2) : 385-412. ScholarBank@NUS Repository. https://doi.org/10.1353/ajm.2008.0010
Abstract: We define and study the set ε(p) of end invariants of an SL(2, ℂ) character p of the one-holed torus T. We show that the set ε(p) is the entire projective lamination space ℘ℒ of T if and only if p corresponds to the dihedral representation or p is real and corresponds to an SU(2) representation; and that otherwise, ε(p) is closed and has empty interior in ℘ℒ. For real characters p, we give a complete classification of ε(p), and show that ε(p) has either 0, 1 or infinitely many elements, and in the last case, ε(p) is either a Cantor subset of ℘ℒ or is ℘ℒ itself. We also give a similar classification for "imaginary" characters where the trace of the commutator is less than 2. Finally, we show that for characters with discrete simple length spectrum (not corresponding to dihedral or SU(2) representations), ε(p) is a Cantor subset of ℘ℒ if it contains at least three elements. © 2008 by The Johns Hopkins University Press.
Source Title: American Journal of Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103199
ISSN: 00029327
DOI: 10.1353/ajm.2008.0010
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