9,934 research outputs found
Wilson surfaces and higher dimensional knot invariants
An observable for nonabelian, higher-dimensional forms is introduced, its
properties are discussed and its expectation value in BF theory is described.
This is shown to produce potential and genuine invariants of higher-dimensional
knots.Comment: 31 pages, 9 figure
Configuration space integrals and invariants for 3-manifolds and knots
The first part of this paper is a short review of the construction
[dg-ga/9710001] of invariants of rational homology 3-spheres and knots in terms
of configuration space integrals.
The second part describes the relationship between the above construction and
Kontsevich's proposal of removing one point from the rational homology sphere.
Explicit formulae are computed. In the case of the "Theta" invariant, a
comparison with Taubes's construction is briefly discussed.Comment: 17 pages, AMS-LaTeX; proceedings of the Madeira conference on "Low
Dimensional Topology," January 199
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
Cabled Wilson Loops in BF Theories
A generating function for cabled Wilson loops in three-dimensional BF
theories is defined, and a careful study of its behavior for vanishing
cosmological constant is performed. This allows an exhaustive description of
the unframed knot invariants coming from the pure BF theory based on SU(2), and
in particular, it proves a conjecture relating them to the Alexander-Conway
polynomial.Comment: 30 pages, LaTe
Pre-Poisson submanifolds
This is an expository and introductory note on some results obtained in
"Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some
original material is contained in the last two sections, where we consider
linear Poisson structures.Comment: Proceedings of the conference "Poisson 2006". 14 page
Wave relations
The wave equation (free boson) problem is studied from the viewpoint of the
relations on the symplectic manifolds associated to the boundary induced by
solutions. Unexpectedly there is still something to say on this simple,
well-studied problem. In particular, boundaries which do not allow for a
meaningful Hamiltonian evolution are not problematic from the viewpoint of
relations. In the two-dimensional Minkowski case, these relations are shown to
be Lagrangian. This result is then extended to a wide class of metrics and is
conjectured to be true also in higher dimensions for nice enough metrics. A
counterexample where the relation is not Lagrangian is provided by the Misner
space.Comment: 27 pages; minor clarifying changes added; to appear in CM
Integral Invariants of 3-Manifolds
This note describes an invariant of rational homology 3-spheres in terms of
configuration space integrals which in some sense lies between the invariants
of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo
Introduction to supergeometry
These notes are based on a series of lectures given by the first author at
the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an
exposition of the theory of super- and graded manifolds, cohomological vector
fields, graded symplectic structures, reduction and the AKSZ-formalism.Comment: Lecture notes of a course held at the school Poisson 2010 at IMPA,
July 2010; 21 pages; references improve
Black Holes and Cosmological Constant in Bosonic String Theory: Some Remarks
(some corrections in the semiclassical study and one reference added).Comment: 17 pages; PHYZZX; IFUM 450/F
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