Date of Award
Spring 2023
Document Type
Thesis
Degree Name
Master of Arts (MA)
Department
Mathematics
Committee Chairperson
Jeremy Brazas, Ph.D.
Committee Member
Shiv Gupta, Ph.D.
Committee Member
Michael Fisher, Ph.D.
Abstract
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
Recommended Citation
Aceti, Johnny, "Higher Spanier Groups" (2023). West Chester University Master’s Theses. 268.
https://digitalcommons.wcupa.edu/all_theses/268