Computing A-Homotopy Groups of Graphs Using Coverings and Lifting Properties
In 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.
A-Homotopy Theory, Discrete Homotopy Theory
Hardeman, 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/33206