Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, February 14, 2022 - 12:00 to 12:50

Location:

WB 205 & Zoom (contact guoren@oregonstate)

Guest Speaker:

Institution:

The University of British Columbia

Abstract:

The knot signature is an important classical invariant of knots which gives a lower bound on the smallest genus of orientable surface a knot can bound in the 4-ball. In this talk I will discuss recent work, some with Ahmad Issa and some with Antonio Alfieri, in which we define an analogous invariant, the equivariant signature, and show that it gives a lower bound on the smallest genus of an invariant surface which a symmetric knot can bound in the 4-ball, for an appropriately restricted class of surfaces. The key technical tool we use is the Atiyah-Singer signature theorem applied to 4-manifolds.