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McShane's identity in rank one symmetric spaces

Published online by Cambridge University Press:  15 April 2014

INKANG KIM ,
JOONHYUNG KIM  and
SER PEOW TAN
INKANG KIM
Affiliation:
School of Mathematics, KIAS, Seoul, 130-722, Korea. e-mail: [email protected]
JOONHYUNG KIM
Affiliation:
Department of Mathematics Education, Hannam University, Daejon 306-791, Republic of Korea. e-mail: [email protected]
SER PEOW TAN
Affiliation:
Department of Mathematics, National University of Singapore, Block S17, Lower Kent Ridge Road, Singapore 119076, Republic of Singapore. e-mail: [email protected]
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Abstract

We study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods unify most of the existing methods used in the existing literature for proving this class of identities.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 1 , July 2014 , pp. 113 - 137
Copyright
Copyright © Cambridge Philosophical Society 2014 

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References

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