Crosscap numbers of a family of Montesinos knots

Abstract

This paper is concerned with the crosscap numbers of Montesinos knots. For a family of Montesinos knots, we give a lower bound of [Formula: see text] among all essential surfaces [Formula: see text] embedded in the exterior, where [Formula: see text] denotes the ratio of negative Euler characteristic of the surface and the number of sheets. From this result, we determine the crosscap numbers of a family of Montesinos knots. Our method relies on the algorithm of enumerating all essential surfaces for Montesinos knots given by Hatcher and Oertel.