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Factorization of homotopies of nanophrases

Published online by Cambridge University Press:  19 October 2011

ANDREW GIBSON
ANDREW GIBSON*
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan. e-mail: gibson@math.titech.ac.jp
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Abstract

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. For any homotopy given by a composite homotopy data triple we define a complete invariant of nanophrases. This invariant is used to show that equivalence of nanophrases under such a homotopy can be calculated just by using the homotopies given by its prime factors.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 1 , January 2012 , pp. 55 - 90
Copyright
Copyright © Cambridge Philosophical Society 2011

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