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Indexed by:期刊论文

Date of Publication:2018-11-01

Journal:JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals:SCIE、Scopus

Volume:27

Issue:13,SI

ISSN No.: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.