The Santa Fe Institute (SFI) hosts “Knots and Links in 4-Dimensions” with Taylor Martin, 12:15 p.m., Wednesday Aug. 12, at Collins Conference Room.
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.