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

TL;DR

This paper introduces link homology theories that categorify quantum link invariants and explores a surprising connection between finite automata and Boolean TQFTs across dimensions.

Contribution

It presents a new perspective linking automata theory with topological quantum field theories and categorification of quantum invariants.

Findings

Connection between finite automata and Boolean TQFTs in dimension one

Development of link homology theories for categorifying Reshetikhin--Turaev invariants

Insights into TQFTs from automata theory

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.