<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>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/14823549 |
| Date | 23 July 2021 |
| Creators | Nathanael D Cox (11008509) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Two_Problems_in_Applied_Topology/14823549 |
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