Classification of curves on surfaces and free links via homotopy theory of words and phrases
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Publication:5171527
DOI10.5427/JSING.2012.6EzbMATH Open1292.57002arXiv0908.2899OpenAlexW2323692476MaRDI QIDQ5171527
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Publication date: 27 July 2014
Published in: (Search for Journal in Brave)
Abstract: V. Turaev introduced the theory of topology of words and phrases in 2005. This is a combinatorialy extension of the theory of virtual knots and links. In this paper we generalize the notion of homotopy of words and phrases and we give geometric meanings of the generalized homotopy of words. Moreover using the generalized homotopy theory of words and phrases, we extend some homotopy invariants of nanophrases to -homotopy invariant of nanowords with some homotopy data .
Full work available at URL: https://arxiv.org/abs/0908.2899
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