Schmutz-Thurston Duality in Mapping Class Group-Equivariant Cell Decompositions

Explore the intricacies of mapping class group-equivariant cell decompositions of Teichmueller space in this 51-minute lecture from the Thematic Programme on "Geometry beyond Riemann: Curvature and Rigidity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the pioneering work of Schmutz and Thurston on closed compact surfaces without marked points. Discover how a special case of Schmutz's construction can be interpreted as dual to Thurston's mapping class group-equivariant spine. Gain insights into the simplified theory of cell decompositions when punctures or marked points are present, and understand the challenges faced when studying surfaces without these features.