Tangle Machines II: Invariants

Avishy Y Carmi, Daniel Moskovich

Research output: Contribution to journalArticle


The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence classes of tangle machines, which are called invariants. This paper constructs invariants of tangle machines. Chief among these are the prime factorizations of a machine, which are essentially unique. This is proven using low dimensional topology, through representing a colour-suppressed machine as a diagram for a network of jointly embedded spheres and intervals in 4-space. The complexity of a tangle machine is defined as its number of prime factors.
Original languageEnglish GB
Number of pages26
JournalarXiv preprint arXiv:1404.2863
StatePublished - 2014


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