Generalizations of Rasmussen's invariant

Abstract: Over the last 20 years, the Rasmussen invariant of knots in $\mathbb{S}^3$ has had a number of interesting applications to questions about surfaces in $\mathbb{B}^4$. In this talk I will survey some recent extensions of the invariant to knots in other three-manifolds: in connected sums of $\mathbb{S}^1$ x $\mathbb{S}^2$ (joint work with Marengon, Sarkar, and Willis), in $\mathbb{RP}^3$ (joint work with Willis, and also separate work of Chen), and in a general setting (work by Morrison, Walker and Wedrich; and independently by Ren-Willis). I will describe how these invariants give bounds on the genus of smooth surfaces in 4-manifolds, and can even detect exotic 4-manifolds with boundary.

geometric topology

Audience: researchers in the topic

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology