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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the mapping class group action on the
cohomology of the representation space
of a surface


Author: Indranil Biswas
Journal: Proc. Amer. Math. Soc. 124 (1996), 1959-1965
MSC (1991): Primary 58D19; Secondary 14D20
MathSciNet review: 1326998
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Abstract: The mapping class group of a $d$-pointed Riemann surface has a natural $C^{\infty }$ action on any moduli space of parabolic bundles with the marked points as the parabolic points. We prove that under some numerical conditions on the parabolic data, the induced action of the mapping class group on the cohomology algebra of the moduli space of parabolic bundles factors through the natural epimorphism of the mapping class group onto the symplectic group.


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Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Bombay 400005, India
Address at time of publication: Institut Fourier des Mathématiques, Université Grenoble I, BP 74, 38402 St. Martin d’Héres-cédex, France
Email: indranil@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03329-1
PII: S 0002-9939(96)03329-1
Keywords: Mapping class group, monodromy, parabolic bundles
Received by editor(s): December 14, 1994
Communicated by: Ronald Stern
Article copyright: © Copyright 1996 American Mathematical Society