Some finite quotients of the mapping class group of a surface

Author:
Patricia L. Sipe

Journal:
Proc. Amer. Math. Soc. **97** (1986), 515-524

MSC:
Primary 32G15; Secondary 57N05

MathSciNet review:
840639

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a smooth, oriented, compact surface of genus , and its Teichmüller modular group (or mapping class group). Let denote the unit tangent bundle, and let be an integer dividing . acts on the finite set , the elements of which are certain homomorphisms from to . In previous work of the author, these homomorphisms arose as the topological description of the th roots of the canonical bundle of the universal Teichmüller curve; however, a topological approach is taken here. The subgroups of which leave all elements of fixed are subgroups of finite index in . Let . The elements of are characterized algebraically. is an extension of by the symplectic group (and in the case of is a semidirect product).

**[1]**Michael F. Atiyah,*Riemann surfaces and spin structures*, Ann. Sci. École Norm. Sup. (4)**4**(1971), 47–62. MR**0286136****[2]**Clifford J. Earle,*Families of Riemann surfaces and Jacobi varieties*, Ann. Math. (2)**107**(1978), no. 2, 255–286. MR**0499328****[3]**-,*Roots of the canonical divisor class over Teichmüller space*, preprint.**[4]**Dennis Johnson,*Spin structures and quadratic forms on surfaces*, J. London Math. Soc. (2)**22**(1980), no. 2, 365–373. MR**588283**, 10.1112/jlms/s2-22.2.365**[5]**W. B. R. Lickorish,*A finite set of generators for the homeotopy group of a 2-manifold*, Proc. Cambridge Philos. Soc.**60**(1964), 769–778. MR**0171269****[6]**David Mumford,*Abelian quotients of the Teichmüller modular group*, J. Analyse Math.**18**(1967), 227–244. MR**0219543****[7]**C. L. Siegel,*Topics in complex function theory. Vol. II*, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Automorphic functions and abelian integrals; Translated from the German by A. Shenitzer and M. Tretkoff; With a preface by Wilhelm Magnus; Reprint of the 1971 edition; A Wiley-Interscience Publication. MR**1008931****[8]**P. L. Sipe,*Roots of the canonical bundle of the universal Teichmüller curve*, Thesis, Cornell Univ., 1979.**[9]**Patricia L. Sipe,*Roots of the canonical bundle of the universal Teichmüller curve and certain subgroups of the mapping class group*, Math. Ann.**260**(1982), no. 1, 67–92. MR**664367**, 10.1007/BF01475756

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
32G15,
57N05

Retrieve articles in all journals with MSC: 32G15, 57N05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0840639-5

Article copyright:
© Copyright 1986
American Mathematical Society