[Geom.,Alg.&Phys.] The formality of the HOMFLYPT skein algebra for surfaces of genus 0
ABSTRACT
In the classical setting, the formality problem of the Goldman--Turaev Lie bialgebra is deeply related to the Kashiwara--Vergne problem by Alekseev--Kawazumi--Kuno--Naef. Recently, for surfaces of genus 0, Bar-Natan--Dancso--Hogan--Liu--Scherich gave an alternative proof of the formality using the Kontsevich integral inspired by Massuyeau's result. In particular, they used the height involution for the Turaev cobracket. On the other hand, Turaev showed that the HOMFLYPT skein algebra is a bi-quantization of the Goldman--Turaev Lie bialgebra. Then, the formality of the HOMFLYPT skein algebra is a natural question. In this talk, we show the formality of the HOMFLYPT skein algebra with respect to the multiplication and the height involution using the Kontsevich integral. This formality can be regarded as a quantization of the result by Bar-Natan et al., i.e. this completely covers their result. This is a joint with Shunsuke Tsuji (Meiji University). (Zoom Meeting ID: 863 9802 5667, Passcode: 490805, link: https://kias-re-kr.zoom.us/j/86398025667?pwd=3J2uAMASqSfwsY6lYyYXPO3R1XHyjx.1) (https://sites.google.com/view/gapkias)
