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PROPERTY (FA) OF THE GAUSS–PICARD MODULAR GROUP

Part of: Riemann surfaces Other groups of matrices

Published online by Cambridge University Press:  15 March 2011

JIEYAN WANG  and
BAOHUA XIE
JIEYAN WANG
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, PR China (email: jywang@hnu.edu.cn)
BAOHUA XIE*
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, PR China (email: xiexbh@gmail.com)
*
✉For correspondence; e-mail: xiexbh@gmail.com
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Abstract

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In this note, we prove that the Gauss–Picard modular group PU(2,1;Θ1) has Property (FA). Our result gives a positive answer to a question by Stover [‘Property (FA) and lattices in SU(2,1)’, Internat. J. Algebra Comput.17 (2007), 1335–1347] for the group PU(2,1;Θ1).

Keywords

Picard modular groupProperty (FA)

MSC classification

Secondary: 30F40: Kleinian groups 20H10: Fuchsian groups and their generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 225 - 228
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work was partially supported by the National Natural Science Foundation of China (No. 11071059) and B. Xie was also supported by Hunan University (No. 531107040021).

References

[1]de la Harpe, P. and Valette, A., ‘La propriété (T) de Kazhdan pour les groupes localement compacts (avec un appendice de Marc Burger)’, Astérisque 175 (1989).Google Scholar
[2]Falbel, E., Francsics, G. and Parker, J. R., ‘The geometry of the Gauss–Picard modular group’, Math. Ann. 349 (2011), 459–508.CrossRefGoogle Scholar
[3]Frohman, C. and Fine, B., ‘Some amalgam structures for Bianchi groups’, Proc. Amer. Math. Soc. 102 (1988), 221–229.CrossRefGoogle Scholar
[4]Goldman, W. M., Complex Hyperbolic Geometry (Oxford University Press, Oxford, 1999).CrossRefGoogle Scholar
[5]Long, D. D., Maclachlan, C. and Reid, A. W., ‘Splitting groups of signature (1;n)’, J. Algebra 185 (1996), 329–341.CrossRefGoogle Scholar
[6]Serre, J.-P., Trees, Springer Monographs in Mathematics (Springer, Berlin, 1980).CrossRefGoogle Scholar
[7]Stover, M., ‘Property (FA) and lattices in SU(2,1)’, Internat. J. Algebra Comput. 17 (2007), 1335–1347.CrossRefGoogle Scholar