The Experts below are selected from a list of 67866 Experts worldwide ranked by ideXlab platform
Edward Witten - One of the best experts on this subject based on the ideXlab platform.
-
eleven dimensional supergravity on a manifold with Boundary
Nuclear Physics, 1996Co-Authors: Petr Hořava, Edward WittenAbstract:Abstract In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with Boundary, which is believed to be relevant to the strong coupling limit of the E 8 × E 8 heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of E 8 for each Boundary Component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum M -theory with eleven-dimensional supergravity as its low-energy limit.
-
eleven dimensional supergravity on a manifold with Boundary
arXiv: High Energy Physics - Theory, 1996Co-Authors: Petr Horava, Edward WittenAbstract:In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with Boundary, which is believed to be relevant to the strong coupling limit of the $E_8\times E_8$ heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of $E_8$ for each Boundary Component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum $M$-theory with eleven-dimensional supergravity as its low energy limit.
Yusuke Kuno - One of the best experts on this subject based on the ideXlab platform.
-
the logarithms of dehn twists
Quantum Topology, 2014Co-Authors: Nariya Kawazumi, Yusuke KunoAbstract:Let Σ be an oriented connected compact surface of genus g (≥ 1) with 1 Boundary Component. Choose a basepoint ∗ ∈ ∂Σ. We denote π := π1(Σ, ∗) and H := H1(Σ;Q). The simple loop going around the Boundary in the opposite direction defines an element ζ ∈ π. Any simple closed curve C ⊂ Σ defines the right handed Dehn twist tC along C as an element of the mapping class group of the surface Σ relative to the Boundary ∂Σ. The classical formula says the action |tC | of the Dehn twist tC on the homology group H is given by |tC | = 1H − [C] ⊗ [C] ∈ Hom(H,H), where [C] ∈ H is the homology class of C with a fixed orientation, and we identify H ⊗H = Hom(H,H), Y ⊗ Z → (X → (X · Y )Z), by the Poincare duality. Our result generalizes this formula to the action of tC on the completed group ring Qπ, where the completion is induced by the augmentation ideal Iπ ⊂ Qπ. Massuyeau [10] introduced the notion of a symplectic expansion of the group π, which provides an isomorphism of pairs of complete Hopf algebras
-
the logarithms of dehn twists
arXiv: Geometric Topology, 2010Co-Authors: Nariya Kawazumi, Yusuke KunoAbstract:By introducing an invariant of loops on a compact oriented surface with one Boundary Component, we give an explicit formula for the action of Dehn twists on the completed group ring of the fundamental group of the surface. This invariant can be considered as ``the logarithms" of Dehn twists. The formula generalizes the classical formula describing the action on the first homology of the surface, and Morita's explicit computations of the extended first and the second Johnson homomorphisms. For the proof we use a homological interpretation of the Goldman Lie algebra in the framework of Kontsevich's formal symplectic geometry. As an application, we prove the action of the Dehn twist of a simple closed curve on the $k$-th nilpotent quotient of the fundamental group of the surface depends only on the conjugacy class of the curve in the $k$-th quotient.
Matthew Jones - One of the best experts on this subject based on the ideXlab platform.
-
compact composition operators with symbol a universal covering map onto a multiply connected domain
Illinois Journal of Mathematics, 2015Co-Authors: Matthew JonesAbstract:We generalise previous results of the author concerning the compactness of composition operators on the Hardy spaces $H^p$, $1\leq p<\infty$, whose symbol is a universal covering map from the unit disk in the complex plane to general finitely connected domains. We demonstrate that the angular derivative criterion for univalent symbols extends to this more general case. We further show that compactness in this setting is equivalent to compactness of the composition operator induced by a univalent mapping onto the interior of the outer Boundary Component of the multiply connected domain.
R C Penner - One of the best experts on this subject based on the ideXlab platform.
-
groupoid extensions of mapping class representations for bordered surfaces
Topology and its Applications, 2009Co-Authors: Jorgen Ellegaard Andersen, Alex James Bene, R C PennerAbstract:Abstract The mapping class group of a surface with one Boundary Component admits numerous interesting representations including a representation as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class group can be identified with the fundamental group of Riemann's moduli space, it is furthermore identified with a subgroup of the fundamental path groupoid upon choosing a basepoint. A combinatorial model for this, the mapping class groupoid, arises from the invariant cell decomposition of Teichmuller space, whose fundamental path groupoid is called the Ptolemy groupoid. It is natural to try to extend representations of the mapping class group to the mapping class groupoid, i.e., to construct a homomorphism from the mapping class groupoid to the same target that extends the given representations arising from various choices of basepoint. Among others, we extend both aforementioned representations to the groupoid level in this sense, where the symplectic representation is lifted both rationally and integrally. The techniques of proof include several algorithms involving fatgraphs and chord diagrams. The former extension is given by explicit formulae depending upon six essential cases, and the kernel and image of the groupoid representation are computed. Furthermore, this provides groupoid extensions of any representation of the mapping class group that factors through its action on the fundamental group of the surface including, for instance, the Magnus representation and representations on the moduli spaces of flat connections.
-
groupoid extensions of mapping class representations for bordered surfaces
arXiv: Geometric Topology, 2007Co-Authors: Jorgen Ellegaard Andersen, Alex James Bene, R C PennerAbstract:The mapping class group of a surface with one Boundary Component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class group can be identified with the fundamental group of Riemann's moduli space, it is furthermore identified with a subgroup of the fundamental path groupoid upon choosing a basepoint. A combinatorial model for this, the mapping class groupoid, arises from the invariant cell decomposition of Teichm\"uller space, whose fundamental path groupoid is called the Ptolemy groupoid. It is natural to try to extend representations of the mapping class group to the mapping class groupoid, i.e., construct a homomorphism from the mapping class groupoid to the same target that extends the given representations arising from various choices of basepoint. Among others, we extend both aforementioned representations to the groupoid level in this sense, where the symplectic representation is lifted both rationally and integrally. The techniques of proof include several algorithms involving fatgraphs and chord diagrams. The former extension is given by explicit formulae depending upon six essential cases, and the kernel and image of the groupoid representation are computed. Furthermore, this provides groupoid extensions of any representation of the mapping class group that factors through its action on the fundamental group of the surface including, for instance, the Magnus representation and representations on the moduli spaces of flat connections.
Petr Hořava - One of the best experts on this subject based on the ideXlab platform.
-
eleven dimensional supergravity on a manifold with Boundary
Nuclear Physics, 1996Co-Authors: Petr Hořava, Edward WittenAbstract:Abstract In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with Boundary, which is believed to be relevant to the strong coupling limit of the E 8 × E 8 heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of E 8 for each Boundary Component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum M -theory with eleven-dimensional supergravity as its low-energy limit.