Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the rotation angles of a finite subgroup of a mapping class group

Kenji Tsuboi

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Abstract

Let $G$ be a finite subgroup of the mapping class group of genus $\sigma$, which acts on a compact Riemann surface of genus $\sigma$. In this paper, we introduce a new method to determine the rotation angle of an element $g\in G$ around the fixed points of $g$. Our main result is Theorem 3.2.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 84, Number 10 (2008), 184-185.

Dates
First available in Project Euclid: 2 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.pja/1228226751

Digital Object Identifier
doi:10.3792/pjaa.84.184

Mathematical Reviews number (MathSciNet)
MR2483564

Zentralblatt MATH identifier
1178.30058

Subjects
Primary: 58C30: Fixed point theorems on manifolds [See also 47H10]
Secondary: 30F99: None of the above, but in this section

Keywords
Riemann surface mapping class group finite group elliptic operator

Citation

Tsuboi, Kenji. On the rotation angles of a finite subgroup of a mapping class group. Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), no. 10, 184--185. doi:10.3792/pjaa.84.184. https://projecteuclid.org/euclid.pja/1228226751


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References

  • E. Bujalance et al., On compact Riemann surfaces with dihedral groups of automorphisms, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 3, 465–477.
  • H. Glover and G. Mislin, Torsion in the mapping class group and its cohomology, J. Pure Appl. Algebra 44 (1987), no. 1–3, 177–189.
  • W. J. Harvey, Cyclic groups of automorphisms of a compact Riemann surface, Quart. J. Math. Oxford Ser. (2) 17 (1966), 86–97.
  • S. P. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), no. 2, 235–265.
  • K. Tsuboi, The finite group action and the equivariant determinant of elliptic operators, J. Math. Soc. Japan 57 (2005), no. 1, 95–113.