Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Spring 2015

Speaker:  Florian Frick, Technische Universität Berlin
Title: From local combinatorics to geometry and topology of manifold triangulations
Time: 2:30 PM, Monday, May 4
Place:  Malott 206

Abstract: Restricting the combinatorics of manifold triangulations might affect the geometry and topology of the underlying manifold. In this talk we will investigate combinatorial restrictions that have an interpretation in terms of curvature: either related to sectional or Ricci curvature by bounding the number of facets around a face of codimension two or related to scalar curvature by bounding the number of facets around a vertex. We give a topological as well as a combinatorial classification of triangulations that are positively curved in the sense of combinatorial sectional curvature. We simplify the proof of a result of Brady, McCammond, and Meier that any closed and orientable 3-manifold has a triangulation with edge-degrees at most six and improve a result of Cooper and Thurston on the number of combinatorial types of vertex links needed to triangulate any closed orientable 3-manifold, which was independently observed by Kevin Walker. This is joint work with Frank Lutz and John M. Sullivan.

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