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Award ID contains: 1821254

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  1. ; (, Topology and its Applications)
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  2. ; ; ; (, Journal of the London Mathematical Society)
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  3. ; ; (, Mathematische Annalen)
    null (Ed.)
    Abstract We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on meridional rank are obtained via Coxeter quotients of the groups of link complements. Matching upper bounds on bridge number are found using the Wirtinger numbers of link diagrams, a combinatorial tool developed by the authors. 
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  4. ; ; ; (, Journal of Topology)
  5. ; ; ; (, Journal of Knot Theory and Its Ramifications)
    We prove that the knots [Formula: see text] and [Formula: see text] both have stick number 10. These are the first non-torus prime knots with more than 9 crossings for which the exact stick number is known. 
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  6. ; (, Journal of the Mathematical Society of Japan)
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  7. ; ; (, Discrete Mathematics)
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  8. ; (, Journal of Knot Theory and Its Ramifications)
    In this paper, we use 3-manifold techniques to illuminate the structure of the category of tangles. In particular, we show that every idempotent morphism [Formula: see text] in such a category naturally splits as [Formula: see text] such that [Formula: see text] is an identity morphism. 
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  9. ; ; (, Journal of Knot Theory and Its Ramifications)
    It was previously shown by the first author that every knot in [Formula: see text] is ambient isotopic to one component of a two-component, alternating, hyperbolic link. In this paper, we define the alternating volume of a knot [Formula: see text] to be the minimum volume of any link [Formula: see text] in a natural class of alternating, hyperbolic links such that [Formula: see text] is ambient isotopic to a component of [Formula: see text]. Our main result shows that the alternating volume of a knot is coarsely equivalent to the twist number of a knot. 
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