Character Variety and Its Algebro-arithmetic Connections to Hyperbolic 3-manifolds

Speaker: 万佳雨 (The Chinese University of Hong Kong)

Time: 2025-12-03 13:00-15:00
Location: 1610, SIMIS

摘要：

The character variety associated with the fundamental group of a hyperbolic 3-manifold M has proven to be a powerful tool in the study of the geometry and topology of M . When the hyperbolic 3-manifold has one cusp, arithmetic tools such as number field and quaternion algebra associated with the character variety can be introduced to extract more geometric and topological information from M . In this talk, we will introduce the concept of character variety and outline the related algebro-arithmetic constructions on hyperbolic 3-manifolds. We will also discuss our recent advancements in generalizing the results to manifolds with multiple cusps.