Stated skein algebras of surfaces

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August undefined, 2024

WebWe study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the … WebApr 25, 2024 · In this paper we study the skein algebras of marked surfaces and the skein modules of marked 3-manifolds. Muller showed that skein algebras of totally marked surfaces may be embedded in easy to study algebras known as quantum tori. We first extend Muller's result to permit marked surfaces with unmarked boundary components.

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WebAbstract. We give a survey of some old and new results about the stated skein modules/algebras of 3-manifolds/surfaces. For generic quantum parameter, we discuss the splitting homomorphism for the 3-manifold case, general structures of the stated skein algebras of marked surfaces (or bordered punctured surfaces) and their embeddings into ... WebSkein definition, a length of yarn or thread wound on a reel or swift preparatory for use in manufacturing. See more. globe iceland tour

Quantum traces and embeddings of stated skein algebras …

WebWe study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the … WebThe stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of … WebMay 9, 2024 · We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming parameter is … globe icon but internet works

On Kauffman bracket skein modules of marked 3–manifolds and …

WebAbstract: The skein algebra of a surface is spanned by links in the thickened surface subject to skein relations. A finer version of the skein algebra, called the stated skein algebra, was introduced by Thang Le and is compatible with the cutting and gluing of surfaces. WebWe study the algebraic and geometric properties of stated skein algebras of surfaces with punctured bounda.ry We prove that the skein algebra of the bigon is iso- morphic to the … boggs family fireWebApr 6, 2024 · We also show that the quantum Teichmüller space of a marked surface, defined by Chekhov–Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra. Keywords Kauffman bracket skein module quantum Teichmüller space quantum trace map MSC classification globe ichthammol

"WebAug 25, 2024 · The skein algebras and modules have played an important role in low-dimensional topology and quantum topology and they serve as a bridge between classical topology and quantum topology. " - Stated skein algebras of surfaces

Stated skein algebras of surfaces

Dimension and Trace of the Kauffman Bracket Skein Algebra

Webskein: [noun] a loosely coiled length of yarn or thread wound on a reel. WebFeb 24, 2016 · Skein algebras of surfaces Jozef H. Przytycki, Adam S. Sikora We show that the Kauffman bracket skein algebra of any oriented surface F (possibly with marked points in its boundary) has no zero divisors and that its center is generated by knots parallel to the unmarked components of the boundary of F.

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WebWe show that the SL_n skein algebra of a surface also has a quantum trace map, which for n=2 is the Bonahon-Wong quantum trace map. The SL_n quantum trace map is constructed via the splitting homomorphism for the stated SL_n skein algebra, developed in joint work with A. Sikora. The Zoom information is listed below: Topic: GW Topology Seminar WebThe stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces...

WebJul 26, 2024 · We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is … WebJul 4, 2024 · François Costantino, Stated skein algebras of surfaces. (Joint work with Thang Le) After providing the definition of stated skein algebras and surfaces and discussing their relations with standard skein algebras, I will state a result detailing their algebraic behavior under topological operations. This, together with the identification of the ...

WebApr 6, 2024 · We survey some old and new results about the stated skein modules of marked 3-manifolds and skein algebras of surfaces. Kauffman bracket skein modules for … WebFeb 1, 2024 · F. Costantino, T. Le Stated Skein algebras of surfaces Received 29 July 2024; accepted 26 October 2024. M. Cossarini, S. Sabourau Minimal area of Finsler disks with minimizing geodesics Received 1 October 2024; accepted 27 February 2024.

WebSpeaker: Francis Bonahon, MSU Title: The quantum trace for skein algebras of surfaces (continued) Date: 02/27/2024 Time: 4:00 PM - 4:30 PM Place: C204A Wells Hall Contact: Michael Shapiro ([email protected]) I will discuss the technical details of the construction of the quantum trace homomorphism, going from the SL_2-skein algebra to the quantum …

WebDec 24, 2016 · The skein algebras were introduced by Przyticki and independently Turaev in an attempt to generalize the Jones polynomial to links in general three-manifolds, and … globe icon search suggestions safari ios boggs family akron ohioWebJan 10, 2024 · The stated skein algebra considered here involves tangles which may end on the boundary of the surface, and is a quotient of a different, larger, stated skein algebra originally considered by Bonahon and Wong. In this paper we study the stated skein modules of marked 3- manifolds. globe icon animation cssWebIt is natural now to study the stated skein algebra of an ideal triangle Tas every repre- ... Skein algebras of surfaces, preprint arXiv:1602.07402, 2016. [SW] A. Sikora and B.W. Westbury ... globe ictWebNov 23, 2024 · The SL (3) skein algebra of a surface is spanned by isotopy classes of Kuperberg's webs in the thickened surface. The product in the skein algebra is given by the superposition of webs. In this talk, we will explore the relationship between these skein algebras and the quantum group associated to SL (3). globe illuminatedWebThe purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms of states as linear functional defined on category algebras. We clarify that category algebras can … boggs family investments edmond oklahomaWebFeb 24, 2016 · Skein algebras of surfaces. We show that the Kauffman bracket skein algebra of any oriented surface F (possibly with marked points in its boundary) has no zero … globe iflix