A Combinatorial Characterization of Geometric 3-Manifolds
Location
383-N
Event Series
Event Type
Seminar
Tuesday, October 12, 2021 4:00 PM
Daryl Cooper (UC Santa Barbara)
Abstract: Given a compact surface, F, and K in {0,1,-1}, the following are equivalent.
- There is a metric of constant curvature K on F.
- There is an immersion of F into the connect sum of (2-K) projective planes.
- There is a triangulation of F such that every vertex has degree (6-K).
We prove similar statements for 3-manifolds, and each of the eight Thurston geometries.
This gives a new algorithm to find a geometric decomposition.
Joint with Priyam Patel.