Release Time:2019-03-13  Hits:

Indexed by: Journal Article

Date of Publication: 2018-11-01

Journal: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals: Scopus、SCIE

Volume: 27

Issue: 13,SI

ISSN: 0218-2165

Key Words: Crosscap number; nonorientable spanning surface; Montesinos knot

Abstract: This paper is concerned with the crosscap numbers of Montesinos knots. For a family of Montesinos knots, we give a lower bound of -chi/#s among all essential surfaces F embedded in the exterior, where -chi/#3 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.