Crosscap numbers and the Jones polynomial

Efstratia Kalfagianni; Christine Ruey Shan Lee

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arXiv · 1408.4493

Crosscap numbers and the Jones polynomial

Efstratia Kalfagianni·Christine Ruey Shan Lee

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Abstract

We give sharp two-sided linear bounds of the crosscap number (non-orientable genus) of alternating links in terms of their Jones polynomial. Our estimates are often exact and we use them to calculate the crosscap numbers for several infinite families of alternating links and for several alternating knots with up to twelve crossings. We also discuss generalizations of our results for classes of non-alternating links.

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Efstratia Kalfagianni, Christine Ruey Shan Lee. 2014-08-19. Crosscap numbers and the Jones polynomial. https://arxiv.org/abs/1408.4493

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