Crosscap number of a knot
type: Item
instance of: scholarly article
title: Crosscap number of a knot
zbMATH Open document ID: 0857.57004
author: Hitoshi Murakami
author: Akira Yasuhara
published in: Pacific Journal of Mathematics
publication date: 1996-11-07T00:00:00Z
review text: \textit{B. E. Clark} [Int. J. Math. Math. Sci. 1, 113-124 (1978; Zbl 0386.57003)] defined the crosscap number of a knot to be the minimum number of the first Betti numbers of non-orientable surfaces bounding it. In this paper, we investigate the crosscap numbers of knots. We show that the crosscap number of \(7_4\) is equal to 3. This gives an affirmative answer to a question given by Clark. In general, the crosscap number is not additive under the connected sum. We give a necessary and sufficient condition for the crosscap number to be additive under the connected sum.
reviewed by: Akira Yasuhara
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 912144
zbMATH Keywords: first Betti numbers
zbMATH Keywords: crosscap numbers
zbMATH Keywords: connected sum
MaRDI profile type: Publication
full work available at URL: pjm.1995.171.261
OpenAlex ID: W1544675568
DOI: 10.2140/PJM.1995.171.261
description: scientific article; zbMATH DE number 912144