Korean Journal of Mathematics

  • 제30권2호
  • /
  • Pages.315-333
  • /
  • 2022
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ℂ-FUCHSIAN SUBGROUPS OF SOME NON-ARITHMETIC LATTICES

  • Sun, Li-Jie (Department of applied science, Yamaguchi University)
  • 투고 : 2022.01.12
  • 심사 : 2022.06.09
  • 발행 : 2022.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We give a general procedure to analyze the structure for certain ℂ-Fuchsian subgroups of some non-arithmetic lattices. We also show their presentations and describe their fundamental domains which lie in a complex geodesic, a set homeomorphic to the unit disk.

키워드

과제정보

The author would like to thank Martin Deraux for drawing her attention to the topic of complex hyperbolic lattices and several valuable discussions. The author is also grateful to Ioannis Platis, Toshiyuki Sugawa for providing helpful comments and suggestions. The author wishes to express her thanks to the referees for their constructive comments which substantially helped improving this paper.

참고문헌

  1. A. F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, 1983.
  2. M. Deraux, Deforming the ℝ-Fuchsian (4, 4, 4)-triangle group into a lattice. Topology, 45 (2006), 989-1020. https://doi.org/10.1016/j.top.2006.06.005
  3. M. Deraux, Non-arithmetic lattices and the klein quartic, J. Reine Angew. Math., 754 (2019), 253-279. https://doi.org/10.1515/crelle-2017-0005
  4. M. Deraux, J. R. Parker, and J. Paupert, New non-arithmetic complex hyperbolic lattices, Invent. Math., 203 (2015), 681-771. https://doi.org/10.1007/s00222-015-0600-1
  5. M. Deraux, J. R. Parker, and J. Paupert, New non-arithmetic complex hyperbolic lattices II, Michigan Math. J., 70 (2021), 135-205.
  6. W. M. Goldman, Complex hyperbolic geometry, Oxford University Press, 1999.
  7. N. Gusevskii and J. R. Parker, Representations of free fuchsian groups in complex hyperbolic space, Topology, 39 (2000), 33-60. https://doi.org/10.1016/S0040-9383(98)00057-3
  8. G. D. Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math., 86 (1980), 171-276. https://doi.org/10.2140/pjm.1980.86.171
  9. J. R. Parker, Unfaithful complex hyperbolic triangle groups. I. Involutions, Pacific J. Math., 238(2008), 145-169. https://doi.org/10.2140/pjm.2008.238.145
  10. J. R. Parker and J. Paupert, Unfaithful complex hyperbolic triangle groups. II. Higher order reflections, Pacific J. Math., 239 (2009), 357-389. https://doi.org/10.2140/pjm.2009.239.357
  11. J. R. Parker and I. D. Platis, Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space, J. Differential Geom., 73 (2006), 319-350.
  12. J. Parkkonen and F. Paulin, A classification of C-Fuchsian subgroups of Picard modular groups, Math. Scand., 121 (2017), 57-74. https://doi.org/10.7146/math.scand.a-26128
  13. R. E. Schwartz, Real hyperbolic on the outside, complex hyperbolic on the inside, Invent. Math., 151 (2003), 221-295. https://doi.org/10.1007/s00222-002-0245-8
  14. M. Stover, Arithmeticity of complex hyperbolic triangle groups, Pacific Journal of Mathematics, 257 (2012), 243-256. https://doi.org/10.2140/pjm.2012.257.243
  15. J. M. Thompson, Complex hyperbolic triangle groups, Doctoral thesis, 2010.
  16. J. Wells, Non-arithmetic hybrid lattices in PU(2, 1), Geom. Dedicata, 208 (2020), 1-11. https://doi.org/10.1007/s10711-019-00506-5