Factorization of homotopies of nanophrases

Details Factorization of homotopies of nanophrases Factorization of homotopies of nanophrases

2009-10-28

arxiv.org/abs/0910.5281v2

Mathematics

Geometric Topology

33 pages, 6 figures. Second version: Improved abstract and introduction

Scientific paper

Homotopy on nanophrases is an equivalence relation defined using some data called a homotopy data triple. We define a product on homotopy data triples. We show that any homotopy data triple can be factorized into a product of prime homotopy data triples and this factorization is unique up to isomorphism and order. If a homotopy data triple is composite, we show that equivalence of nanophrases under the corresponding homotopy can be calculated just by using the homotopies given by its prime factors.

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