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

Abstract

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 ≥ 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.