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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. [Copyright &y& Elsevier]

Abstract: We obtain a characterization of the isotropy lattice for the lifted action of a Lie group G on TM and based only on the knowledge of G and its action on M. Some applications to symplectic geometry are also shown. To cite this article: M. Rodríguez-Olmos, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]