Itsy bitsy topological field theory

TL;DR

This paper develops a simple, combinatorial topological quantum field theory based on curves and surfaces, inspired by contact invariants in sutured Floer homology, embodying a digital 'it from bit' concept.

Contribution

It introduces a new combinatorial TQFT that encodes information digitally and extends Honda--Kazez--Matic's framework, linking topological invariants with quantum information concepts.

Findings

Constructs a combinatorial TQFT based on curves and surfaces.

Provides a binary information storage model on surfaces.

Features digital creation and annihilation operators.

Abstract

We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of a TQFT defined by Honda--Kazez--Matic. This topological field theory stores information in binary format on a surface and has "digital" creation and annihilation operators, giving a toy-model embodiment of "it from bit".