Discrete Morse Theory by Vector Fields: A Survey and New Directions

Author

Matthew Nemitz, Minnesota State University, Mankato

Abstract

We synthesize some of the main tools in discrete Morse theory from various sources. We do this in regards to abstract simplicial complexes with an emphasis on vector fields and use this as a building block to achieve our main result which is to investigate the relationship between simplicial maps and homotopy. We use the discrete vector field as a catalyst to build a chain homotopy between chain maps induced by simplicial maps.

Advisor

Brandon Rowekamp

Committee Member

Wook Kim

Committee Member

Ke Zhu

Date of Degree

2020

Language

english

Document Type

APP

Degree

Master of Science (MS)

Department

Mathematics and Statistics

College

Science, Engineering and Technology

Recommended Citation

Nemitz, M. (2020). Discrete Morse theory by vector fields: A survey and new directions [Master’s alternative plan paper, Minnesota State University, Mankato]. Cornerstone: A Collection of Scholarly and Creative Works for Minnesota State University, Mankato. https://cornerstone.lib.mnsu.edu/etds/986/

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.