Rank of 3-Manifold Groups - Part I

Explore the concept of rank in 3-manifold groups in this comprehensive lecture from the Workshop on Groups around 3-Manifolds. Begin with a brief discussion on the general notion of rank in groups before delving into its specific applications in 3-manifold groups. Examine the relationship between rank and Heegaard genus, and investigate the work of Abert-Nikolov connecting rank growth in cover towers to the "cost" of certain measured equivalence relations. Discover insights from the speaker's collaborative work with Souto on ranks of mapping tori with large curve complex translation distance, as well as geometric decompositions of thick hyperbolic 3-manifolds with bounded rank. Gain a deeper understanding of this fundamental concept in 3-manifold theory through this 57-minute presentation by Ian Biringer at the Centre de recherches mathématiques.