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An Invariant of Surfaces Embedded in the 3-Sphere
Preprint
26 April 2020
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Abstract
A closed connected orientable surface embedded in the 3-sphere S3 splits it into two submanifolds. On the other hand, Heegaard splittings of each submanifold give us a pair of handlebody-knots (a two-component handlebody-link). In this paper, we construct an invariant of such surfaces by using an invariant of handlebody-knots derived from quandles. We compute our invariant in the case of bi-knotted surfaces.