Friday, Oct 27, 2017 - 3:00pm - Allen 14
Detecting Local Properties of Fundamental Groups
Dr. Jeremy Brazas, Mathematics, West Chester University
Title: Detecting Local Properties of Fundamental Groups
Abstract: The algebraic structure of the fundamental group of a path-connected metric space X often depends heavily on the local structure of X. Roughly speaking, to verify local properties that characterize this kind of dependence, it is necessary to detect the existence of a specific homotopy given a certain, possibly infinite, arrangement of paths. In this talk I'll discuss joint work with Hanspeter Fischer that introduces a unified approach to characterizing and comparing a number of these properties by constructing closure operators on the π1-subgroup lattice in terms of maps from a fixed “test" domain.
Biography: Dr. Brazas received his Ph.D. in Mathematics from the University of New Hampshire in 2011 under the advisement of Dr. Maria Basterra. His primary research focus is in the area of algebraic topology. He is currently an Assistant Professor at West Chester University in West Chester, Pennsylvania.