Spherical Knot Mosaics

Abstract

In this paper we introduce the notion of a spherical knot mosaic where a knot is represented by tiling the surface of an n by n by n topological 2-sphere with 11 canonical knot mosaic tiles and show this gives rise to several novel knot (and link) invariants: the spherical mosaic number, spherical tiling number, minimal spherical mosaic tile number, spherical face number, spherical n-mosaic face number, and minimal spherical mosaic face number. We show examples where this framework is an improvement over classical knot mosaics. Furthermore, we explore several bounds involving other classical knot invariants that these spherical mosaic invariants gives rise to.

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