# Singular Poisson reduction of cotangent bundles.

Simon Hochgerner; Armin Rainer

Revista Matemática Complutense (2006)

- Volume: 19, Issue: 2, page 431-466
- ISSN: 1139-1138

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topHochgerner, Simon, and Rainer, Armin. "Singular Poisson reduction of cotangent bundles.." Revista Matemática Complutense 19.2 (2006): 431-466. <http://eudml.org/doc/41909>.

@article{Hochgerner2006,

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.},

author = {Hochgerner, Simon, Rainer, Armin},

journal = {Revista Matemática Complutense},

keywords = {Geometría simpléctica; Variedades de Poisson; Espacios y haces de fibras; Weinstein space; singular reduction; momentum map},

language = {eng},

number = {2},

pages = {431-466},

title = {Singular Poisson reduction of cotangent bundles.},

url = {http://eudml.org/doc/41909},

volume = {19},

year = {2006},

}

TY - JOUR

AU - Hochgerner, Simon

AU - Rainer, Armin

TI - Singular Poisson reduction of cotangent bundles.

JO - Revista Matemática Complutense

PY - 2006

VL - 19

IS - 2

SP - 431

EP - 466

AB - 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.

LA - eng

KW - Geometría simpléctica; Variedades de Poisson; Espacios y haces de fibras; Weinstein space; singular reduction; momentum map

UR - http://eudml.org/doc/41909

ER -