Titlebook: Lectures in Knot Theory; An Exploration of Co Józef H. Przytycki,Rhea Palak Bakshi,Deborah Weeks Textbook 2024 The Editor(s) (if applicable

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Józef H. Przytycki,Rhea Palak Bakshi,Dionne Ibarra,Gabriel Montoya-Vega,Deborah Weeksexes and saturation of dangling bonds as a result, has contributed to a great interest in the hydrogen passivation process. From a technological point of view, the hydrogen passivation plays an important role both at the growth and the processing phases of the semiconductor bulk material. From a fun

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Spin Structure and the Framing Skein Module of Links in 3-Manifolds,h background information on non-separating spheres, Dehn homeomorphisms, and mapping class groups of 3-manifolds. The main tools used in the proof are based on Darryl McCullough’s work on the mapping class groups of 3-manifolds and spin structures. We then relate these results to the theory of skein modules.

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The Witten-Reshetikhin-Turaev Invariants of 3-Manifolds,y. In this lecture, we focus on W. B. Raymond Lickorish’s Kauffman bracket skein theoretic approach to the invariants. In the last section of this lecture, we introduce a skein module described by Justin Roberts that incorporates the Jones-Wenzl idempotents and has close connections to the (2 + 1)-TQFT and WRT invariants.

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Gram Determinants of Type , and Type ,hin-Turaev invariant of 3-manifolds. We then discuss the Gram determinant of type .b where the closure is taken in a Möbius band. We state some results that support the closed formula for this Gram determinant conjectured by Q. Chen in 2009.

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Khovanov Homology: A Categorification of the Jones Polynomial,taining more information, and having a richer algebraic structure. One of the spectacular applications of Khovanov homology is that it detects the unknot. In this lecture, we present an elementary exposition of Khovanov homology following the construction by Oleg Viro.

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