Homotopy invariants of Gauss words

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

By defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to show that there exist Gauss words that are not homotopically equivalent to the empty Gauss word, disproving a conjecture by Turaev. In fact, we show that there are an infinite number of equivalence classes of Gauss words under homotopy.
15 pages, 4 figures. Second version: added reference, corrected some comments

Keywords

Geometric Topology, 57M99 (Primary); 68R15 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/229738

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0902.0062
 http://arxiv.org/abs/0902.0062

Collections

arXiv