Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 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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