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Two Problems in Applied Topology

<div>In this thesis, we present two main results in applied topology.</div><div> In our first result, we describe an algorithm for computing a semi-algebraic description of the quotient map of a proper semi-algebraic equivalence relation given as input. The complexity of the algorithm is doubly exponential in terms of the size of the polynomials describing the semi-algebraic set and equivalence relation.</div><div> In our second result, we use the fact that homology groups of a simplicial complex are isomorphic to the space of harmonic chains of that complex to obtain a representative cycle for each homology class. We then establish stability results on the harmonic chain groups.</div>

  1. 10.25394/pgs.14823549.v1
Identiferoai:union.ndltd.org:purdue.edu/oai:figshare.com:article/14823549
Date23 July 2021
CreatorsNathanael D Cox (11008509)
Source SetsPurdue University
Detected LanguageEnglish
TypeText, Thesis
RightsCC BY 4.0
Relationhttps://figshare.com/articles/thesis/Two_Problems_in_Applied_Topology/14823549

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