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On the mapping class group action on the cohomology of the representation space of a surface
Author(s):
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  -pointed Riemann surface has a natural  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.
References:
- [BR]
- Biswas, I., Raghavendra, N. : Canonical generators of the cohomology of moduli of parabolic bundles on curves, Math. Ann. (to appear).
- [DS]
- Dostoglou, S., Salamon, D. : Self-dual instantons and holomorphic curves. Ann. Math. 139 (1994) 581--640. CMP 94:15
- [KT]
- Kamber, F., Tondeur, P. : Foliated bundles and characteristic classes. Lec. Notes in Math. Vol. 493. Springer-Verlag. MR 53:6587
- [MS]
- Mehta, V., Seshadri, C.S. : Moduli of vector bundles on curves with parabolic structure. Math. Ann. 248 (1980) 205--239. MR 81i:14010
- [S]
- Simpson, C.T. : Harmonic bundles on noncompact curves. Jour. Amer. Math. Soc. 3 (1990) 713--770. MR 91h:58029
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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