Graduate Thesis Or Dissertation

 

Homology Representations Arising from a Hypersimplex Público Deposited

https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/nc580m66v
Abstract
  • 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.
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  • 2011
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  • 2019-11-16
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