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Congruence Link Complements—A 3-Dimensional Rademacher Conjecture

  • M. D. Baker
  • A. W. ReidEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 245)

Abstract

In this article we discuss a 3-dimensional version of a conjecture of Rademacher concerning genus 0 congruence subgroups of \(\mathrm{PSL}(2,\mathbb Z)\). We survey known results, as well as including some new results that make partial progress on the conjecture.

Keywords

Link complement Bianchi group Congruence subgroup 

Notes

Acknowledgements

The work contained in this paper was developed over multiple visits to the University of Texas by the first author, and the Université de Rennes 1 by the second author. We also wish to thank the Université Paul Sabatier, the Max Planck Institüt, Bonn, I.C.T.P. Trieste and The Institute for Advanced Study for their support and hospitality as this work unfolded over several years. We also wish to thank several people without whose help we would not have been able to complete this work: M. D. E. Conder, D. Holt, M. Goerner, E. O’Brien, A. Page, M. H. Sengun and A. Williams. We also thank I. Agol, N. Hoffman and P. Sarnak for useful conversations on topics related to this work. We are also very grateful to the referee for their comments and helpful suggestions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IRMARUniversité de Rennes 1Rennes CedexFrance
  2. 2.Department of MathematicsRice UniversityHoustonUSA

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