An application of non-positively curved cubings of alternating links

Sakuma, Makoto; Yokota, Yoshiyuki

doi:10.1090/proc/13918

An application of non-positively curved cubings of alternating links
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by Makoto Sakuma and Yoshiyuki Yokota PDF

Proc. Amer. Math. Soc. 146 (2018), 3167-3178 Request permission

Abstract:

By using non-positively curved cubings of prime alternating link exteriors, we prove that certain ideal triangulations of their complements, derived from reduced alternating diagrams, are non-degenerate, in the sense that none of the edges is homotopic relative its endpoints to a peripheral arc. This guarantees that the hyperbolicity equations for those triangulations for hyperbolic alternating links have solutions corresponding to the complete hyperbolic structures. Since the ideal triangulations considered in this paper are often used in the study of the volume conjecture, this result has a potential application to the volume conjecture.

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