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Classifications of star products and deformations of Poisson brackets

Philippe Bonneau (2000)

Banach Center Publications

On the algebra of functions on a symplectic manifold we consider the pointwise product and the Poisson bracket; after a brief review of the classifications of the deformations of these structures, we give explicit formulas relating a star product to its classifying formal Poisson bivector.

Cocalibrated G 2 -manifolds with Ricci flat characteristic connection

Thomas Friedrich (2013)

Communications in Mathematics

Any 7-dimensional cocalibrated G 2 -manifold admits a unique connection with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of -parallel vector fields.

Cocycle condition for multi-pullbacks of algebras

Piotr M. Hajac, Bartosz Zieliński (2012)

Banach Center Publications

Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorphism. We note that this gluing procedure does not guarantee that the building pieces, or the gluings of some pieces, are embedded in the space obtained by putting together all given ingredients. Dually, we show that a certain sufficient condition, called the cocycle condition, is also necessary to guarantee sheaf-like properties of surjective multi-pullbacks...

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