Itsy bitsy topological field theory

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".

54 pages, 35 figures. Minor edits, extra figures added

References in corpus (5)

• Contact structures, sutured Floer homology and TQFT
• Bordered Floer homology for sutured manifolds
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Joining and gluing sutured Floer homology
• The cylindrical contact homology of universally tight sutured contact solid tori

Cited by in corpus (8)

• Dimensionally-reduced sutured Floer homology as a string homology
• Contact categories of disks
• Twisty itsy bitsy topological field theory
• Strand algebras and contact categories
• Tight contact structures on Seifert surface complements
• Combinatorial Sutured TQFT as Exterior Algebra
• On the decategorification of some higher actions in Heegaard Floer homology
• A-infinity algebras, strand algebras, and contact categories