Full paper in PDF:
$% S. Hochgerner and A. Rainer, Singular Poisson reduction of cotangent bundles, Rev. Mat. Complut. 19 (2006), no. 2, 431–466.%$

Singular Poisson Reduction of Cotangent Bundles
Simon HOCHGERNER and Armin RAINER
Institut für Mathematik
Universität Wien
Nordbergstrasse 15
A-1090 Vienna — Austria
simon.hochgerner@univie.ac.at  armin.rainer@univie.ac.at

Received: January 23, 2006
Accepted: May 19, 2006

ABSTRACT

We consider the Poisson reduced space * (T Q)/K , where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to * T Q . Realizing * (T Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q-> Q/K which are of single orbit type.

Key words: cotangent bundle reduction, singular reduction, Poisson structures.
2000 Mathematics Subject Classication: 53D17, 53D20.