The standardness conjecture for (b;b1,c2,c3)(b;b-1,c_2,c_3)-bridge trisections

Let K\mathcal{K} be a knotted surface in S4S^4 admitting a (b;b1,c2,c3)(b;b-1,c_2,c_3)--bridge trisection. Such a bridge trisection is a surface of the indicated type, with bb the bridge parameter and c2,c3c_2,c_3 the remaining parameters. Standardness conjecture. Every (b;b1,c2,c3)(b;b-1,c_2,c_3)--surface is an unlink of unknotted 2--spheres and at most one unknotted projective plane. The conjecture is motivated by the fact that the associated branched double-cover trisection is standard; the source presents the corresponding conclusion as reasonable to conjecture, without stating a resolution.

Sources & referencesView supporting material

Primary source

Jeffrey Meier and Alexander Zupan, “Bridge trisections of knotted surfaces in S^4”, arXiv:1507.08370 (2015).

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