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University of Colorado

1. Harper, Jacob Tyler. Homology Representations Arising from a Hypersimplex.

Degree: PhD, Mathematics, 2011, University of Colorado

We present a complete acyclic matching of the Hasse diagram associated with the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. We will then utilize this matching along with discrete Morse theory and some topological techniques to classify every subcomplex whose reduced homology groups are concentrated in a single degree. These reduced homology groups support a natural action of the symmetric group and a description of the characters that this action produces is given. Advisors/Committee Members: Richard M. Green, Nathaniel Thiem, Marty Walter.

Subjects/Keywords: Subcomplexes; homology Representations; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Harper, J. T. (2011). Homology Representations Arising from a Hypersimplex. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/9

Chicago Manual of Style (16th Edition):

Harper, Jacob Tyler. “Homology Representations Arising from a Hypersimplex.” 2011. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020. https://scholar.colorado.edu/math_gradetds/9.

MLA Handbook (7th Edition):

Harper, Jacob Tyler. “Homology Representations Arising from a Hypersimplex.” 2011. Web. 30 Oct 2020.

Vancouver:

Harper JT. Homology Representations Arising from a Hypersimplex. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2020 Oct 30]. Available from: https://scholar.colorado.edu/math_gradetds/9.

Council of Science Editors:

Harper JT. Homology Representations Arising from a Hypersimplex. [Doctoral Dissertation]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/math_gradetds/9

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