Research ArticleNo Access

Raising crosscap number while lowering unknotting number

Ave Maria University, 5050 Ave Maria Blvd, Ave Maria, FL 34142-9505, USA

E-mail Address: anne.kerian@avemaria.edu

https://doi.org/10.1142/S0218216520500303Cited by:1 (Source: Crossref)

Abstract

We explore the relationship between two knot invariants, unknotting number and crosscap number. Specifically, we present two infinite families of knots with a specific crossing change that lowers the unknotting number while raising the crosscap number. One of these families is hyperbolic. This is a non-orientable parallel of Scharlemann and Thompson’s 1988 result for orientable surfaces.

Keywords:

AMSC: 57K10

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