COLIN ADAMS, ZACHARY ROMRELL, ALEXANDRA BONAT, MAYA CHANDE, JOYE CHEN, MAXWELL JIANG, DANIEL SANTIAGO, BENJAMIN SHAPIRO, DORA WOODRUFF
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Abstract
In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints which here we call poles. We define generalised knotoids to allow arbitrarily many poles, intervals and circles, each pole corresponding to any number of interval endpoints, including zero. This theory subsumes a variety of other related topological objects and introduces some particularly interesting new cases. We explore various analogs of knotoid invariants, including height, index polynomials, bracket polynomials and hyperbolicity. We further generalise to knotoidal graphs, which are a natural extension of spatial graphs that allow both poles and vertices.
期刊介绍：
Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.
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