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On Fenchel–Nielsen Coordinates of Surface Group Representations into SU(3,1)

Published online by Cambridge University Press:  01 March 2017

KRISHNENDU GONGOPADHYAY  and
SHIV PARSAD
KRISHNENDU GONGOPADHYAY
Affiliation:
Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, S.A.S. Nagar 140306, Punjab, India. e-mail: [email protected], [email protected]
SHIV PARSAD
Affiliation:
Indian Institute of Science Education and Research (IISER) Bhopal, Bhopal Bypass Road, Bhauri Bhopal 462 066 Madhya Pradesh, India. e-mail: [email protected]
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Abstract

Let Σg be a compact, connected, orientable surface of genus g ≥ 2. We ask for a parametrisation of the discrete, faithful, totally loxodromic representations in the deformation space Hom(π1(Σg), SU(3, 1))/SU(3, 1). We show that such a representation, under some hypothesis, can be determined by 30g − 30 real parameters.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 1 , July 2018 , pp. 1 - 23
Copyright
Copyright © Cambridge Philosophical Society 2017 

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