Date/Time
Date(s) - 13/11/2025
3:30 pm - 4:30 pm

Speaker: William Menasco (University at Buffalo)

Location: Hamilton Hall, Room 312

Title: A Seifert algorithm for integral homology spheres. Joint work with Linda Alegria.

Abstract: From classical knot theory we know that every knot in $S^3$ is the boundary of an oriented, embedded surface. A standard demonstration of this fact achieved by elementary technique comes from taking a regular projection of any knot and employing Seifert’s constructive algorithm. In this note we give a natural generalization of Seifert’s algorithm to any closed integral homology 3-sphere. The starting point of our algorithm is presenting the handle structure of a Heegaard splitting of a given integral homology sphere as a planar diagram on the boundary of a $3$-ball. (For a well known example of such a planar presentation, see the Poincar\’e homology sphere planar presentation in {\em Knots and Links} by D. Rolfsen \cite{Rolfsen}.) An oriented link can then be represented by the regular projection of an oriented $k$-strand tangle. From there we give a natural way to find a “Seifert circle” and associated half-twisted bands.