Computing A-Homotopy Groups of Graphs Using Coverings and Lifting Properties

dc.contributor.advisorBauer, Kristine
dc.contributor.advisorSeyffarth, Karen
dc.contributor.authorHardeman, Rachel
dc.contributor.committeememberLaflamme, Claude
dc.contributor.committeememberCunningham, Clifton
dc.date2018-11
dc.date.accessioned2018-10-12T14:54:21Z
dc.date.available2018-10-12T14:54:21Z
dc.date.issued2018-09-21
dc.description.abstractIn classical homotopy theory, two spaces are homotopy equivalent if one space can be continuously deformed into the other. This theory, however, does not respect the discrete nature of graphs. For this reason, a discrete homotopy theory that recognizes the difference between the vertices and edges of a graph was invented, called A-homotopy theory. In classical homotopy theory, covering spaces and lifting properties are often used to compute the fundamental group of a space. In this thesis, we develop the lifting properties for A-homotopy theory. Using a covering graph and these lifting properties, we compute the fundamental group of the cycle C_5 and use this computation to show that C_5 is not contractible in this theory, even though the cycles C_3 and C_4 are contractible.en_US
dc.identifier.citationHardeman, R. (2018). Computing A-Homotopy Groups of Graphs Using Coverings and Lifting Properties (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/33206en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/33206
dc.identifier.urihttp://hdl.handle.net/1880/108868
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.facultyScience
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectA-Homotopy Theory
dc.subjectDiscrete Homotopy Theory
dc.subject.classificationMathematicsen_US
dc.titleComputing A-Homotopy Groups of Graphs Using Coverings and Lifting Properties
dc.typemaster thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.item.requestcopytrue
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