An Infinite Family of Links with Critical Bridge Spheres

Daniel Rodman

doi:10.2140/agt.2018.18.153

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arXiv · 1602.05512

An Infinite Family of Links with Critical Bridge Spheres

Daniel Rodman

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Abstract

A closed, orientable, splitting surface in an oriented $3$-manifold is a topologically minimal surface of index $n$ if its associated disk complex is $(n-2)$-connected but not $(n-1)$-connected. A critical surface is a topologically minimal surface of index $2$. In this paper, we use an equivalent combinatorial definition of critical surfaces to construct the first known critical bridge spheres for nontrivial links.

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Daniel Rodman. 2016-02-17. An Infinite Family of Links with Critical Bridge Spheres. https://doi.org/10.2140/agt.2018.18.153

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