A Combinatorial Characterization of Geometric 3-Manifolds - Lecture

Explore a groundbreaking approach to understanding geometric 3-manifolds in this 52-minute lecture from the Workshop on Groups around 3-Manifolds. Delve into joint preliminary work by Priyam Patel, D. Cooper, and L. Mavrakis that introduces the concept of "locally combinatorially defined" (LCD) geometries. Discover how this novel approach leads to a new algorithm for finding geometric decompositions of 3-manifolds and a method for constructing random 3-manifolds. Examine motivating examples that illustrate the definition of LCD families of spaces. Gain insights into the crucial role of branched 3-manifolds in this innovative approach, with a focus on proving results for select geometries. Enhance your understanding of the Geometrization Theorem and its implications for the canonical decomposition of closed 3-manifolds into pieces with Thurston geometries.