"Cycle decomposition for integral current homology" by Kristin Julia Duling

Semester

Fall

Date of Graduation

2022

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Mathematics

Committee Chair

Jerzy Wojciechowski

Committee Co-Chair

Krzysztof Ciesielski

Committee Member

Krzysztof Ciesielski

Committee Member

Elaine Eschen

Committee Member

Hong-Jian Lai

Committee Member

Michael Mays

Abstract

A standard graph theoretical result states that every element of the cycle space of a graph has a cycle decomposition. Georgakopoulos expands this result to a primitive decomposition and minimal representation of each element in a modified 1-dimensional singular homology. We modify the m-dimensional integral current homology in order to ensure a primitive decomposition for each element.

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