Abstracts
for the Seminar

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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