Date of Award

Spring 2023

Document Type


Degree Name

Master of Arts (MA)



Committee Chairperson

Jeremy Brazas, Ph.D.

Committee Member

Shiv Gupta, Ph.D.

Committee Member

Michael Fisher, Ph.D.


When non-trivial local structures are present in a topological space X, a common ap- proach to characterizing the isomorphism type of the n-th homotopy group πn(X, x0) is to consider the image of πn(X, x0) in the n-th ˇCech homotopy group ˇπn(X, x0) under the canonical homomorphism Ψn : πn(X, x0) → ˇπn(X, x0). The subgroup ker Ψn is the obstruc- tion to this tactic as it consists of precisely those elements of πn(X, x0), which cannont be detected by polyhedral approximations to X. In this paper we present a definition of higher dimensional analouges of Thick Spanier groups use higher dimensional Spanier groups to characterize ker Ψn. In particular, we prove that if X is paracompact, Hausdroff, and UVn−1, then ker Ψn is equal to the n-th Spanier group of X. We also use the perspec- tive of higher Spanier groups to generalize a theorem of Kozlowski-Segal, which gives conditions to ensure that Ψn is an isomorphism