13,201 research outputs found
Deformation Quantization and Reduction
This note is an overview of the Poisson sigma model (PSM) and its
applications in deformation quantization. Reduction of coisotropic and
pre-Poisson submanifolds, their appearance as branes of the PSM, quantization
in terms of L-infinity and A-infinity algebras, and bimodule structures are
recalled. As an application, an "almost" functorial quantization of Poisson
maps is presented if no anomalies occur. This leads in principle to a novel
approach for the quantization of Poisson-Lie groups.Comment: 23 pages, 3 figures; added references, corrected typo
Tulczyjew's triples and lagrangian submanifolds in classical field theories
In this paper the notion of Tulczyjew's triples in classical mechanics is
extended to classical field theories, using the so-called multisymplectic
formalism, and a convenient notion of lagrangian submanifold in multisymplectic
geometry. Accordingly, the dynamical equations are interpreted as the local
equations defining these lagrangian submanifolds.Comment: 29 page
Embedded Cobordism Categories and Spaces of Manifolds
Galatius, Madsen, Tillmann and Weiss have identified the homotopy type of the
classifying space of the cobordism category with objects (d-1)-dimensional
manifolds embedded in R^\infty. In this paper we apply the techniques of spaces
of manifolds, as developed by the author and Galatius, to identify the homotopy
type of the cobordism category with objects (d-1)-dimensional submanifolds of a
fixed background manifold M.
There is a description in terms of a space of sections of a bundle over M
associated to its tangent bundle. This can be interpreted as a form of Poincare
duality, relating a space of submanifolds of M to a space of functions on M
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