Fuchsian moduli on a Riemann surface—its Poisson structure and Poincaré-Lefschetz duality

Katsunori Iwasaki

Vol. 155 (1992), No. 2, 319–340

DOI: 10.2140/pjm.1992.155.319

Abstract

The moduli space of Fuchsian projective connections on a closed Riemann surface admits a Poisson structure. The moduli space of projective monodromy representations on the punctured Riemann surface also admits a Poisson structure which arises from the Poincaré-Lefschetz duality for cohomology. We shall show that the former Poisson structure coincides with the pull-hack of the latter by the projective monodromy map. This result explains intrinsically why a Hamiltonian structure arises in the monodromy preserving deformation.

Mathematical Subject Classification 2000

Primary: 32G34

Secondary: 14D20, 58F05

Milestones

Received: 29 April 1991

Published: 1 October 1992