SMS scnews item created by Haotian Wu at Thu 2 Mar 2017 1053
Type: Seminar
Distribution: World
Expiry: 1 Sep 2017
Calendar1: 9 Mar 2017 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Geometry & Toplogy Seminar: Boris Lishak -- Complexity of untying 2-knots
Auth: haotianw@130.56.25.44 (hawu2800) in SMS-WASM

# Complexity of untying 2-knots

### Boris Lishak (Sydney)

Thursday 9 March 12:00–13:00 in Carslaw 535A.

Abstract: Embeddings of $S^2$ into $S^4$ can be topologically nontrivial. But even if the embedding is trivial, geometrically it can "look" knotted. We will give examples of topologically trivial $2$-knots such that their complexity will grow super-exponentially. Complexity will be either defined in terms of Riemannian geometry in the smooth case or combinatorially if the embedding is piece-wise linear. Proofs will use some group theory.