On the complexity of 2-bridge link complements

James Morgan; Jonathan Spreer

doi:10.2140/agt.2026.26.2315

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arXiv · 2406.09629

On the complexity of 2-bridge link complements

James Morgan·Jonathan Spreer

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Abstract

We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string braid construction. For the 2-bridge links satisfying this condition we construct explicit angle structures on the Sakuma-Weeks triangulations and compute both multiplicative and additive lower bounds on the complexity of the link complements via volume estimates. These lower bounds are an improvement on existing volume estimates for the 2-bridge links examined.

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James Morgan, Jonathan Spreer. 2024-06-13. On the complexity of 2-bridge link complements. https://doi.org/10.2140/agt.2026.26.2315

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