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Award ID contains: 2231492

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  1. ; ; ; ; ; ; ; ; ; ; et al (, International Journal of Algebra and Computation)
    Genevois recently classified which graph braid groups are word hyperbolic. In the 3-strand case, he asked whether all such word hyperbolic groups are actually free; this reduced to checking two infinite classes of graphs: sun and pulsar graphs. We prove that 3-strand braid groups of sun graphs are free. On the other hand, it was known to experts that 3-strand braid groups of most pulsar graphs contain surface subgroups. We provide a simple proof of this and prove an additional structure theorem for these groups. 
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    Free, publicly-accessible full text available May 1, 2026
  2. (, Journal of Knot Theory and Its Ramifications)
    The non-orientable 4-genus of a knot [Formula: see text] in [Formula: see text] is defined to be the minimum first Betti number of a non-orientable surface [Formula: see text] smoothly embedded in [Formula: see text] so that [Formula: see text] bounds [Formula: see text]. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We will also view obstructions to a knot bounding a Möbius band given by the double branched cover of [Formula: see text] branched over [Formula: see text]. 
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    Free, publicly-accessible full text available January 1, 2026