Introduction to Computational Topology Using Simplicial Persistent Homology

Author

Jason Turner, Union College - Schenectady, NYFollow
Brenda Johnson, Union College - Schenectady, NYFollow
Ellen Gasparovic, Union College - Schenectady, NYFollow

Date of Award

3-2018

Document Type

Open Access

Degree Name

Bachelor of Science

Department

Mathematics

First Advisor

Brenda Johnson

Second Advisor

Ellen Gasparovic

Language

English

Keywords

algebraic, topology, persistent, homology, simplicial, complex, buckyballs

Abstract

The human mind has a natural talent for finding patterns and shapes in nature where there are none, such as constellations among the stars. Persistent homology serves as a mathematical tool for accomplishing the same task in a more formal setting, taking in a cloud of individual points and assembling them into a coherent continuous image. We present an introduction to computational topology as well as persistent homology, and use them to analyze configurations of BuckyBalls®, small magnetic balls commonly used as desk toys.

Recommended Citation

Turner, Jason; Johnson, Brenda; and Gasparovic, Ellen, "Introduction to Computational Topology Using Simplicial Persistent Homology" (2018). Honors Theses. 1660.
https://digitalworks.union.edu/theses/1660