Invariants of $2$-knots

Abstract

This short survey, which was written to accompany a minicourse at the BIRS conference 'Topology in dimension 4.5', concerns invariants of knotted 2-spheres in S 4 , also known as 2-knots. It covers invariants extracted from the algebraic topology of the knot exterior, including Alexander invariants, the Farber-Levine pairing and Casson-Gordon invariants, as well as gauge theoretic and combinatorial invariants. Details are scarce and new results inexistant.