摘要：The SL2(C) character variety, particularly the canonical component containing the character of a particular discrete faithful representation, has emerged as an important tool in studying the topology of hyperbolic 3-manifolds. Chinburg-Reid-Stover constructed arithmetic invariants stemming from a canonical Azumaya algebra over the projectivization of the canonical component. We provide an explicit topological criterion for extending the canonical Azumaya algebra over an ideal point, potentially leading to finer arithmetic invariants. Along the way, we use techniques and arguments of Paoluzzi-Porti and Tillmann to show that certain families of once-punctured tori in knot complements are detected by an ideal point of the character variety and that in this case, refined Chinburg-Reid-Stover invariants exist.
邀请人：张影