Taylor Martin (Sam Houston State University)
Abstract. The mathematical branch of topology is the study of the properties of shape that are unchanged by stretching. One aspect of topology is the study of knots and links. A mathematical knot is an embedding of a circle into 3-dimensional space, while a link is an embedding of more than one circle into 3-space. One way to study knots and links is to give them a group structure – a way to “multiply” them – called smooth knot and link concordance. The link concordance group is a very large group with unknown structure. To better understand this group, Cochran, Orr, and Teichner defined the n-solvable filtration in 2003, which is a filtration of the link concordance group that can be thought of as a way to approximate how “close” a link is to bounding disks in 4-dimensional space. In this talk, we will discuss the study of links, introduce link concordance, and give new results about the n-solvable filtration.