**SMS scnews item created by Boris Lishak at Wed 21 Aug 2019 1146**

Type: Seminar

Distribution: World

**Calendar1: 2 Sep 2019 1200-1300**

**CalLoc1: Carslaw 535A**

CalTitle1: Singh -- Knotted Surfaces in 4-manifolds and Distances Between Them

Auth: borisl@dora.maths.usyd.edu.au

### Geometry and Topology Seminar

# Knotted Surfaces in 4-manifolds and Distances Between Them

### Oliver Singh (Durham)

September 2, 12:00-13:00 in Carslaw 535
Seminar schedule

Please join us for lunch after the talk.

**Abstract:**
I will discuss knotted surfaces, isotopy classes of embedded surfaces in a given 4-manifold, and will define two notions of distance between them. These distances are integer-valued and are defined topologically: one in terms of regular homotopy; another in terms of stabilisation, a form of embedded surgery. I will outline a proof of an inequality between these distances; the proof is constructive and draws upon ideas pioneered by Gabai in the proof of the 4-dimensional light bulb theorem.