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Stability of Universal Constructions for Persistent Homology

thesis
posted on 01.08.2019 by Janis Lazovskis
In this thesis I describe poset stratifications of the product of the Ran space and the nonnegative real numbers, as a universal space for the Cech construction of simplicial complexes. This leads to a cosheaf valued in diagrams of simplicial complexes for which every restriction to a finite collection recovers the persistent homology of the collection. For the stratification, I describe a partial order on isomorphism classes of abstract simplicial complexes, which allows spaces stratified by them to have entrance paths uniquely interpreted as simplicial maps. Decomposing entrance paths gives a sheaf structure, which has higher information that the cosheaf does not capture.

History

Advisor

Antieau, David Benjamin

Chair

Antieau, David Benjamin

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Degree name

PhD, Doctor of Philosophy

Committee Member

Shipley, Brooke Groves, Daniel Weinberger, Shmuel Curry, Justin

Submitted date

August 2019

Thesis type

application/pdf

Language

en

Issue date

14/06/2019

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