2018-2019 Faculty Research Grants
Anthony Bosman (Mathematics)
Families of Links Related by Band Surgery
Links are mathematical objects studied in knot theory. An m-component link is an embedding of m disjoint circles into 3-dimensional space such that they are each possibly knotted and linked to one another. A knot is a 1-component link. Building on my doctoral work, this knot theory project will analyze the impact of an operation called band surgery on families of links. Band surgery can be used to reduce the abstract 4-dimensional operations of link concordance and shake concordance to simple 2-dimensional diagrammatic moves. As such, it allows undergraduates with limited formal training to participate in otherwise high-level research. Support for this project will allow me to extend a number of results from my dissertation resulting in new publications in respected topology journals and presentations at regional and national math conferences/seminars. Also, it will mentor undergraduates in mathematics research, leading to (co)authored undergraduate publications and presentations. Knot theory is an especially active area of undergraduate research with journals and a conference devoted to undergraduate work in knot theory; this grant will aid in firmly establishing Andrews’ presence and reputation in this research community in the upcoming years.