Abstracts
for the Seminar

Fall 2016

**Speaker: **Ed Swartz, Cornell University

**Title: **Sometimes more is less

**Time:** 2:30 PM, Monday, October 3, 2016

**Place:** Malott 206

**Abstract:** How do we understand the complexity of a space? When the space can be triangulated by a finite complex, one possible avenue to measuring its complexity is to look at the number of faces needed to triangulate it. We will concentrate on this approach as it applies to 3-dimensional manifolds and 3-dimensional normal pseudomanifolds. Along the way we will see: 1) How some of the usual measures of topological complexity, such as Betti numbers, are related to the combinatorial complexity of its triangulations. 2) Whether we currently know more about minimal triangulations of 3-manifolds or 3-pseudomanifolds depends on the types of triangulations allowed. 3) An example whose topological complexity does not appear to be in sink with its combinatorial complexity.
Some of this work is joint work with Tair Akhmejanov and Saromoira Shields.

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