4 papers
Topological Data Analysis of Mortality Patterns During the COVID-19 Pandemic
Megan Fairchild, Matthew Lemoine
Topological Data Analysis is a relatively new field of study that uses topological invariants to study the shape of data. We analyze a dataset provided by the Centers for Disease C…
Whitehead Doubles and Non-Orientable Surfaces
Megan Fairchild
Whitehead doubles provide a plethora of examples of knots that are topologically slice but not smoothly slice. We discuss the problem of the Whitehead double of the Figure 8 knot a…
Non-orientable 4-genus of torus knots
Megan Fairchild, Hailey Jay Garcia, Jake Murphy +1
The non-orientable 4-genus of a knot in , denoted , measures the minimum genus of a non-orientable surface in bounded by . We compute bounds for the n…
The Non-Orientable 4-Genus of 11 Crossing Non-Alternating Knots
Megan Fairchild
The non-orientable 4-genus of a knot K in the three sphere is defined to be the minimum first Betti number of a non-orientable surface F in the four-ball so that K bounds F. We wil…