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Representations of the Kauffman bracket skein algebra of the punctured torus

Jea-Pil Cho, Răzvan Gelca (2014)

Fundamenta Mathematicae

We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary.

Representing open 3-manifolds as 3-fold branched coverings.

José María Montesinos-Amilibia (2002)

Revista Matemática Complutense

It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S3, and in some cases, a 2-fold branched covering of S3. The branching set is a locally finite disjoint union of strings.

Residues for monogenic forms on Riemannian manifolds

Souček, Vladimír (1994)

Proceedings of the Winter School "Geometry and Physics"

The paper extends the theory of residues on monogenic forms on domains in n (monogenic forms are generalizations of holomorphic forms to Clifford analysis) to monogenic forms on orientable Riemann manifolds.

Résidus des connexions à singularités et classes caractéristiques

Daniel Lehmann (1981)

Annales de l'institut Fourier

Un “théorème des résidus” est donné, qui exprime les classes caractéristiques réelles de dimension 2 k d’un fibré principal C à l’aide d’une connexion définie seulement au-dessus d’un voisinage du ( 2 k - 1 ) -squelette d’une triangulation de la base. Ce théorème coiffe simultanément la théorie de Chern-Weil, la théorie de l’obstruction modulo torsion, ainsi que des formules du type Riemann-Hurwitz pour les revêtements ramifiés.

Résidus des sous-variétés invariantes d'un feuilletage singulier

Daniel Lehmann (1991)

Annales de l'institut Fourier

Une formule de résidus est demontrée pour les classes caractéristiques de degré suffisamment grand du fibré normal à une sous variété lisse V d’une variété W , invariante relativement à un feuilletage avec singularités dans W . En particulier, dans le cas analytique complexe, et pour les feuilletages dont les feuilles sont de dimension complexe 1, les nombres de Chern du fibre normal à la sous-variété V sont calculés en termes de résidus de Grothendieck, par une formule qui généralise au cas de dimensions...

Resolutions of moduli spaces and homological stability

Oscar Randal-Williams (2016)

Journal of the European Mathematical Society

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and gives explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.

Resurgence of the Kontsevich-Zagier series

Ovidiu Costin, Stavros Garoufalidis (2011)

Annales de l’institut Fourier

The paper is concerned with the resurgence of the Kontsevich-Zagier series f ( q ) = n = 0 ( 1 - q ) ( 1 - q n ) We give an explicit formula for the Borel transform of the power series when q = e 1 / x from which its analytic continuation, its singularities (all on the positive real axis) and the local monodromy can be manifestly determined. We also give two formulas (one involving the Dedekind eta function, and another involving the complex error function) for the right, left and median summation of the Borel transform. We also prove that the...

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