Peripheral structures of core groups

Daniel S. Silver; Lorenzo Traldi

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arXiv · 2504.06365

Peripheral structures of core groups

Daniel S. Silver·Lorenzo Traldi

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Abstract

The core group is an invariant of unoriented virtual links. We introduce a peripheral structure for the core group, in which the longitudes are sensitive to orientations. We show that the combination of the core group and its peripheral structure is equivalent, as a link invariant, to the combination of the $\pi$-orbifold group and its peripheral structure. Examples show that the peripheral structure of the core group can be used to verify noninvertibility of some knots and links.

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Daniel S. Silver, Lorenzo Traldi. 2025-04-08. Peripheral structures of core groups. https://arxiv.org/abs/2504.06365

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