Classification of curves on surfaces and free links via homotopy theory of words and phrases

Tomonori Fukunaga

Journal of Singularities
volume 6 (2012), 37-53
Proceedings of the Workshop on Singularities in Geometry and Applications, Będlewo, 5 – 21 May 2011

Received: 30 December 2011. Received in revised form: 12 May 2012.

DOI: 10.5427/jsing.2012.6e

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Abstract:

In this paper, we introduce Turaev's homotopy theory of words and phrases. As new results, we give the classification of oriented ordered pointed irreducible multi-component curves on surfaces which is called monoliteral type with at most six crossings up to stably equivalence using Turaev's homotopy theory of words and phrases. Moreover we also give the classification of (oriented) ordered pointed irreducible free links of monoliteral type with at most six crossings.

Keywords:

étale phrases, nanophrases, curves on surfaces, stably equivalent

Mathematical Subject Classification:

Primary 57M99; Secondary 68R15

Author(s) information:

Tomonori Fukunaga
Department of Mathematics
Hokkaido University
Sapporo 060-0810, Japan
email: fukunaga@math.sci.hokudai.ac.jp