2024/12/28 by Jumpei Yasuda, Yasuda, Jumpei
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2412.20081
openalex publication_date 2024/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The knot group is the fundamental group of a knot or link complement. A necessary and sufficient conditions for a group to be realized as the knot group of some link was provided. This result was shown using the closed braid method. González-Acuña and Kamada independently extended this characterization to the knot groups of orientable surface-links. Kamada applied the closed 2-dimensional braid method to show this result. In this paper, we generalize these results to characterize the knot groups of surface-links, including non-orientable ones. We use a plat presentation for surface-links to prove it. Furthermore, we show a similar characterization for the knot symmetric quandles of surface-links. As an application, we show that every dihedral quandle with an arbitrarily good involution can be realized as the knot symmetric quandle of a surface-link.