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A lower bound of crosscap numbers of alternating knots

Noboru Ito

http://orcid.org/0000-0001-9011-8982

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153-8914, Japan

E-mail Address: noboru@ms.u-tokyo.ac.jp

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and

Yusuke Takimura

Gakushuin Boys’ Junior High School, 1-5-1 Mejiro, Toshima-ku, Tokyo, 171-0031, Japan

E-mail Address: Yusuke.Takimura@gakushuin.ac.jp

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https://doi.org/10.1142/S0218216519500925Cited by:2 (Source: Crossref)

Abstract

We give a lower bound of the crosscap number of alternating knots using band surgery. This lower bound is equal to the minimum number of the first Betti number, i.e. one minus the maximal Euler characteristic, over all (orientable and non-orientable) surfaces spanning a given alternating knot.

Keywords:

AMSC: 57M25

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