A Kind of Essential Surfaces in the Complements of Knots (Communications in Mathematical Research, 2021)
In this paper, by the twist-crossing number of knots, we give an upperbound on the Euler characteristic of a kind of essential surfaces in the complementsof alternating knots and almost alternating knots, which improves the estimation ofthe Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.
Keywords: essential surface; twist-crossing number; almost alternating knot; reduced graph.