From finite state automata to tangle cobordisms: a TQFT journey from one to four dimensions

Abstract

This is a brief introduction to link homology theories that categorify Reshetikhin--Turaev $\mathsf{SL}(N)$-quantum link invariants. A recently discovered surprising connection between finite state automata and Boolean TQFTs in dimension one is explained as a warm-up.

40 pages, many figures, corrected minor misprints. To appear in Contemporary Mathematics, conference proceedings "From Representation Theory to Mathematical Physics and Back"