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Integral Riemann–Roch formulae for cyclic subgroups of mapping class groups

  • TOSHIYUKI AKITA (a1) and NARIYA KAWAZUMI (a2)

Abstract

The first author conjectured certain relations for Morita–Mumford classes and Newton classes in the integral cohomology of mapping class groups (integral Riemann–Roch formulae). In this paper, the conjecture is verified for cyclic subgroups of mapping class groups.

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[1]Akita, T.. Nilpotency and triviality of mod p Morita–Mumford classes of mapping class groups of surfaces. Nagoya Math. J. 165 (2002), 122.
[2]Akita, T., Kawazumi, N. and Uemura, T.. Periodic surface automorphisms and algebraic independence of Morita–Mumford classes. J. Pure Appl. Algebra 160 (2001), 111.
[3]Earle, C. J. and Eells, J.. A fibre bundle description of Teichmüller theory. J. Differential Geom. 3 (1969), 1943.
[4]Farkas, H. M. and Kra, I.. Riemann Surfaces (2nd ed.). GTM 71 (Springer–Verlag, 1992).
[5]Galatius, S., Madsen, Ib and Tillmann, U.. Divisibility of the stable Miller–Morita-Mumford classes. J. Amer. Math. Soc. 19 (2006), 759779.
[6]Glover, H. H., Mislin, G. and Xia, Y.. On the Yagita invariant of mapping class groups. Topology 33 (1994), 557574.
[7]Harer, J. L.. The second homology group of the mapping class group of an oriented surface. Invent. Math. 72 (1983), 221239.
[8]Ireland, K. and Rosen, M.. A Classical Introduction to Modern Number Theory (2nd ed.). GTM 84 (Springer–Verlag, 1981).
[9]Kawazumi, N.. Weierstrass points and Morita–Mumford classes on hyperelliptic mapping class groups. Topology Appl. 125 (2002), 363383.
[10]Kawazumi, N. and Uemura, T.. Riemann–Hurwitz formula for Morita–Mumford classes and surface symmetries. Kodai Math. J. 21 (1998), 372380.
[11]Morita, S.. Characteristic classes of surface bundles. Invent. Math. 90 (1987), 551577.
[12]Mumford, D.. Towards an enumerative geometry of the moduli space of curves. In Arithmetic and Geometry Vol. II (Birkhäuser, 1983), pp. 271328.
[13]Nielsen, J.. The structure of periodic surface transformations. In Jakob Nielsen: Collected Mathematical Papers Vol. 2 (Birkhäuser, 1986), pp. 65102.
[14]Porubský, Š.. Voronoĭ's congruence via Bernoulli distributions. Czechoslovak Math. J. 34 (109) (1984), 15.
[15]Porubský, Š.. Voronoi type congruences for Bernoulli numbers. In Voronoi's Impact on Modern Science Book 1 (Institute of Mathematics of the National Academy of Sciences of Ukraine, 1998), pp. 7198.
[16]Symonds, P.. The cohomology representation of an action of C p on a surface. Trans. Amer. Math. Soc. 306 (1988), 389400.
[17]Thomas, C. B.. Characteristic Classes and Cohomology of Finite Groups. Cambridge Studies in Advanced Mathematics 9 (Cambridge University Press, 1986).

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