A lower bound of crosscap numbers of alternating knots-Reference-Cited by-同舟云学术

A lower bound of crosscap numbers of alternating knots

Published:2020-01 Issue:01 Volume:29 Page:1950092
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Ito Noboru¹^ORCID,Takimura Yusuke²

Affiliation:

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216519500925

Reference15 articles.

1. A classification of spanning surfaces for alternating links

2. Knot Enumeration Through Flypes and Twisted Splices

3. Crosscaps and knotes

4. Incompressible surfaces in 2-bridge knot complements

5. Crosscap numbers of 2-bridge knots

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1. Crosscap number three alternating knots;Journal of Knot Theory and Its Ramifications;2022-04

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3. Crosscap numbers of alternating knots via unknotting splices;International Journal of Mathematics;2020-06-25