1,720,978 research outputs found
Reidemeister\u27s theorem using transversality
Full text linkWe recover Reidemeister\u27s theorem using smooth functions and transversality.My goal here was to give an easily readable proof for the Reidemeister theorem based on transversality techniques. I hope it can prove useful when learning or teaching knot theory, or as a gentle introduction to the use of transversality for knots and knotted surfaces. The paper will appear in the Bulletin of the Australian Mathematical Societ
Reidemeister’s theorem using transversality
No full textInternational audienceWe recover Reidemeister’s theorem using smooth functions and transversality
Polynomial link invariants and quantum algebras
No full textInternational audienceThe definition of the Jones polynomial in the 80's gave rise to a large family of so-called quantum link invariants, based on quantum groups. These quantum invariants are all controlled by the same two-variable invariant (the HOMFLY-PT polynomial), which also specializes to the older Alexander polynomial. Building upon quantum Schur--Weyl duality and variants of this phenomenon, I will explain an algebraic setup that allows for global definitions of these quantum polynomials, and discuss extensions of these quantum objects designed to encompass all of the mentioned invariants, including the HOMFLY-PT polynomial
Khovanov-Seidel braid representation
Full text linkThese are lecture notes from a lecture series given at CIRM in the Fall 2023.
They give a down-to-earth introduction to Khovanov and Seidel's categorical
representation of Artin-Tits groups, emphasizing the fact that it is all
explicitly computable. Several prospective applications to (geometric) group
theory are mentioned.Comment: Lecture notes from the CIRM conference "Current trends in
representation theory, cluster algebras and geometry", November 2023.
Comments welcome
Gl2 Foam Functoriality and Skein Positivity
No full text71 pages. Preliminary version, comments welcome!We prove full functoriality of Khovanov homology for tangled framed gl2 webs. We use this functoriality result to prove a strong positivity result for (orientable) surface skein algebras. The argument goes categorical and consists in proving that so-called linear complexes are stable under superposition
Gl2 Foam Functoriality and Skein Positivity
Full text linkWe prove full functoriality of Khovanov homology for tangled framed gl2 webs.
We use this functoriality result to prove a strong positivity result for
(orientable) surface skein algebras. The argument goes categorical and consists
in proving that so-called linear complexes are stable under superposition.Comment: 71 pages. Preliminary version, comments welcome
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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