LAZOVSKIS-DISSERTATION-2019.pdf (918.28 kB)
Download fileStability of Universal Constructions for Persistent Homology
thesis
posted on 2019-08-01, 00:00 authored by Janis LazovskisIn 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 BenjaminChair
Antieau, David BenjaminDepartment
Mathematics, Statistics, and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral
Degree name
PhD, Doctor of PhilosophyCommittee Member
Shipley, Brooke Groves, Daniel Weinberger, Shmuel Curry, JustinSubmitted date
August 2019Thesis type
application/pdfLanguage
- en