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On the geometry of reduced cotangent bundles at zero momentum
Authors:Matthew Perlmutter  Miguel Rodríguez-Olmos  M Esmeralda Sousa-Dias
Institution:Dep. Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Abstract:We consider the problem of cotangent bundle reduction for proper non-free group actions at zero momentum. We show that in this context the symplectic stratification obtained by Sjamaar and Lerman refines in two ways: (i) each symplectic stratum admits a stratification which we call the secondary stratification with two distinct types of pieces, one of which is open and dense and symplectomorphic to a cotangent bundle; (ii) the reduced space at zero momentum admits a finer stratification than the symplectic one into pieces that are coisotropic in their respective symplectic strata.
Keywords:53D20  37J15
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