LdT Seminar Doubleheader 1 (Wednesday March 26th).

[Rafael Torres]

Speaker: Sebastián Matías Camponovo (UniTS)

Title: On Codimension-Two Embeddings of Spheres

Abstract: One of the fundamental questions in knot theory is determining homotopical criteria on the knot exterior that can "detect" the unknot. Papakyriakopoulos resolved the classical case in 1957, showing that the unknot is the only knot whose complement has the integers as its fundamental group.
In 1964 Levine provided analogous criteria in higher dimensional knot theory in the smooth category: an n-knot, for n≥4, is unknotted if and only if its exterior is homotopy equivalent to a circle. In 1968, Julius Shaneson extended this criterion to 3-knots embedded in S^5.
In this seminar, we will follow his work and examine his proof of this result. This discussion will lead us to two related topics: the effect of surgery on the unknotted n-knot and the h-cobordism theorem for S^1×S^3.


Date: Wednesday March 26th, 2025
Time: 11:00 am
Venue: Room 004