Conjugacy classes of the hyperelliptic mapping class group of genus 2 and 3. (English) Zbl 0958.57018

Ahara, Kazushi; Takasawa, Mitsuhiko

Exp. Math. 9, No. 3, 383-396 (2000).

Summary: We present tables of conjugacy classes of the hyperelliptic mapping class group of genus 2 and 3, and some theorems on the Sp representation, the Jones representation, and Meyer’s function.

MSC:

57N05	Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57M50	General geometric structures on low-dimensional manifolds

Keywords:

Siegel modular group; Thurston type; Jones representation; Meyer’s function

References:

[1]	Birman j. S., Ann. of Math. (2) 97 pp 424– (1973) · Zbl 0237.57001 · doi:10.2307/1970830
[2]	Endo H., Math. Ann. 316 (2) pp 237– (2000) · Zbl 0948.57013 · doi:10.1007/s002080050012
[3]	Humphries S. P., Topology of low-dimensional manifolds (Chelwood Gate, Sussex, 1977) pp 44– (1979) · doi:10.1007/BFb0063188
[4]	Jones V. F. R., Ann. Of Math. (2) 126 (2) pp 335– (1987) · Zbl 0631.57005 · doi:10.2307/1971403
[5]	Kazhdan D., Invent. Math. 53 (2) pp 165– (1979) · Zbl 0499.20035 · doi:10.1007/BF01390031
[6]	Lickorish W. B. R., Proc. Cambridge Philos. Soc. 60 pp 769– (1964) · doi:10.1017/S030500410003824X
[7]	Lickorish W. B. R., Proc. Cambridge Philos. Soc. 60 pp 769– (1964)
[8]	Matsumoto M., Math. alnn. 316 (3) pp 401– (2000) · Zbl 0968.57014 · doi:10.1007/s002080050336
[9]	Meyer W., Math. Ann. 201 pp 239– (1973) · Zbl 0241.55019 · doi:10.1007/BF01427946
[10]	Ochiai M., Experiment. Math. 4 (1) pp 61– (1995) · Zbl 0846.20016 · doi:10.1080/10586458.1995.10504308
[11]	Penner R. C., Combinatorics of train tracks, Ann. Math. Studies 125 (1992) · Zbl 0765.57001 · doi:10.1515/9781400882458
[12]	Thurston W. P., Bull. Amer. Math. Soc. (N.S.) 19 (2) pp 417– (1988) · Zbl 0674.57008 · doi:10.1090/S0273-0979-1988-15685-6
[13]	Wajnryb B., Israel J. Math. 45 (2) pp 157– (1983) · Zbl 0533.57002 · doi:10.1007/BF02774014
[14]	Wenzl H., Invent. Math. 92 (2) pp 349– (1988) · Zbl 0663.46055 · doi:10.1007/BF01404457