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论文类型：期刊论文

发表时间：2018-11-01

发表刊物：JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

收录刊物：SCIE、Scopus

卷号：27

期号：13,SI

ISSN号：0218-2165

关键字：Crosscap number; nonorientable spanning surface; Montesinos knot

摘要：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.