Compactification of $\operatorname{SL}(3,\mathbb{C})$-Character Varieties of Surfaces via Skein Algebras

Source abstract

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.