Good involutions of generalized Alexander quandles
Yuta Taniguchi
TL;DR
This paper characterizes and classifies all good involutions of connected generalized Alexander quandles, providing a foundation for their use in defining invariants of unoriented knots and links.
Contribution
It establishes the necessary and sufficient conditions for the existence of good involutions and classifies all such involutions up to isomorphism.
Findings
Derived conditions for good involutions in generalized Alexander quandles
Classified all good involutions of connected generalized Alexander quandles
Enhanced understanding of symmetric quandles for knot invariants
Abstract
Quandles with good involutions, which are called symmetric quandles, can be used to define invariants of unoriented knots and links. In this paper, we determine the necessary and sufficient condition for good involutions of a generalized Alexander quandle to exist. Moreover, we classify all good involutions of a connected generalized Alexander quandle up to symmetric quandle isomorphisms.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology