Countable Groups as Fundamental Groups of Compacta in Four-Dimensional Euclidean Space

Author

Ziga Virk, University of Tennessee - Knoxville

Date of Award

8-2009

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Jerzy Dydak

Committee Members

Carl Sundberg, Morwen Thistlethwaite, Russell Zaretzki, Nikolay Brodskiy

Abstract

This dissertation addresses the question of realization of countable groups as funda- mental groups of continuum. In first chapter we discuss classical realizations in the category of CW complexes. We introduce Eilenberg-Maclane spaces and their topological properties. The second chapter provides recent developments on realization question such as those of Shelah, Keesling, ... The third chapter proves the realization theorem for countable groups. The re- sulting space is compact path connected, connected subspace of four dimensional Euclidean space.

Recommended Citation

Virk, Ziga, "Countable Groups as Fundamental Groups of Compacta in Four-Dimensional Euclidean Space. " PhD diss., University of Tennessee, 2009.
https://trace.tennessee.edu/utk_graddiss/79