# Coisotropic submanifolds and the BFV-complex

Schätz, F. Coisotropic submanifolds and the BFV-complex. 2009, University of Zurich, Faculty of Science.

## Abstract

Coisotropic submanifolds form an important class of subobjects of Poisson manifolds. In this thesis two algebraic structures associated to coisotropic submanifolds are constructed and their properties are investigated. First we explain the construction of the homotopy Lie algebroid – following Oh, Park and Cattaneo, Felder, respectively. The invariance of the homotopy Lie algberoid is established. This part of the thesis relies on joint work with Cattaneo. Next the BFV-complex is introduced. To this end we give a new conceptual construction of the BFV-bracket. The dependence of the BFV-complex on certain input data is clarified. Moreover an L1 quasi-isomorphism between the homotopy Lie algebroid and the BFV-complex is constructed. Finally we connect the BFV-complex with the local deformation theory of coisotropic submanifolds. It turns out that the BFV-complex allows to construct a groupoid which is isomorphic to the deformation groupoid of the coisotropic submanifold.

## Abstract

Coisotropic submanifolds form an important class of subobjects of Poisson manifolds. In this thesis two algebraic structures associated to coisotropic submanifolds are constructed and their properties are investigated. First we explain the construction of the homotopy Lie algebroid – following Oh, Park and Cattaneo, Felder, respectively. The invariance of the homotopy Lie algberoid is established. This part of the thesis relies on joint work with Cattaneo. Next the BFV-complex is introduced. To this end we give a new conceptual construction of the BFV-bracket. The dependence of the BFV-complex on certain input data is clarified. Moreover an L1 quasi-isomorphism between the homotopy Lie algebroid and the BFV-complex is constructed. Finally we connect the BFV-complex with the local deformation theory of coisotropic submanifolds. It turns out that the BFV-complex allows to construct a groupoid which is isomorphic to the deformation groupoid of the coisotropic submanifold.

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### Citations

11 citations in Microsoft Academic

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