Physical Sciences and Mathematics Commons^™

Discrete Morse Theory By Vector Fields: A Survey And New Directions, Matthew Nemitz

All Graduate Theses, Dissertations, and Other Capstone Projects

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.