Infinite sequences of mutually non-conjugate surface braids representing same surface-links

Iwakiri, Masahide

doi:10.1090/S0002-9939-2011-10893-1

Infinite sequences of mutually non-conjugate surface braids representing same surface-links
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Proc. Amer. Math. Soc. 140 (2012), 357-366 Request permission

Abstract:

We give an infinite sequence of mutually non-conjugate surface braids with same degree representing the trivial surface-link with at least two components and a pair of non-conjugate surface braids with same degree representing a spun $(2,t)$-torus knot for $t\geq 3$. To give these examples, we introduce new invariants of conjugacy classes of surface braids via colorings by Alexander quandles or core quandles of groups.

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