On the complexity of 2-bridge link complements

Morgan, James; Spreer, Jonathan

doi:10.2140/agt.2026.26.2315

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On the complexity of $2$-bridge link complements

James Morgan and Jonathan Spreer

Algebraic & Geometric Topology 26 (2026) 2315–2352

DOI: 10.2140/agt.2026.26.2315

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.

Keywords

2-manifold, minimal triangulation, complexity, 2-bridge link, angle structure, hyperbolic volume

Mathematical Subject Classification

Primary: 57Q15

Secondary: 57K10, 57K31, 57K32

References

Publication

Received: 22 August 2024

Revised: 24 March 2025

Accepted: 15 April 2025

Published: 22 June 2026

Authors

James Morgan
School of Mathematics and Statistics The University of Sydney Sydney Australia

Jonathan Spreer
School of Mathematics and Statistics The University of Sydney Sydney Australia

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Volume 26, issue 6 (2026)