H(2)-Unknotting Operation Related to 2-Bridge Links
Yuanyuan Bao
TL;DR
This paper investigates the H(2)-unknotting numbers of links related to 2-bridge links, providing conditions, explicit forms, and methods for studying these invariants in complex links and knots.
Contribution
It offers a necessary and sufficient condition for 2-bridge links to have H(2)-unknotting number one, explicit forms of certain composite links, and a new method for analyzing tangle unknotting numbers.
Findings
Characterization of 2-bridge links with H(2)-unknotting number one
Explicit forms of composite links with H(2)-unknotting number one
A method for studying H(2)-unknotting numbers of tangle unknotting number one knots
Abstract
This paper concerns the H(2)-unknotting numbers of links related to 2-bridge links. It consists of three parts. In the first part, we consider a necessary and sufficient condition for a 2-bridge link to have H(2)-unknotting number one. The second part concerns an explicit form of composite links with H(2)-unknotting number one. In the last part, we develop a method of studying the H(2)-unknotting numbers of some tangle unknotting number one knots via 2-bridge knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Homotopy and Cohomology in Algebraic Topology