On the complexity of 2-bridge link complements

2024/06/13 by Morgan, James, Spreer, Jonathan
#57K10 #57K31 #57K32 #57Q15 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2406.09629

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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