arXiv subjects
Publications and source records attributed to Seong Youn Kim.
We investigate the filtration structure of the skein algebra induced by the (quantum) trace map. Utilizing the structure, we prove that relative $\operatorname{SL}(3, \mathbb{C})$ character varieties of punctured surfaces admit log Calabi-Yau compactifications and prove the (weak) geometric P=W conjecture.
Let $g, n \geq 0$ and $Σ= Σ_{g, n}$ be a connected oriented surface of genus $g$ with $n$ punctures. The $\mathrm{SL}_2$-character variety of $Σ$ has a rigid relative automorphism group, whose elements fix each monodromies along punctures, and is a finite extension of the mapping class group. The exceptional isomorphism between the $\mathrm{SL}(2, \mathbb{C})$-character variety and moduli of points on complex $3$-sphere provides a new description of the mapping class group of certain $Σ$.