Prime amphicheiral knots with free period 2
Luisa Paoluzzi, Makoto Sakuma
TL;DR
This paper constructs prime amphicheiral knots with free period 2, addressing an open question about the existence of such knots with specific symmetry properties.
Contribution
It provides the first known examples of prime amphicheiral knots with free period 2, filling a gap in the understanding of knot symmetries.
Findings
Prime amphicheiral knots with free period 2 are constructed.
Addresses an open question in knot theory.
Shows such knots can exist despite previous restrictions.
Abstract
We construct prime amphicheiral knots that have free period 2. This settles an open question raised by the second named author, who proved that amphicheiral hyperbolic knots cannot admit free periods and that prime amphicheiral knots cannot admit free periods of order >2.
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