Structure and unique factorization in concordance groups of links

Kouki Sato; Akira Yasuhara

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arXiv · 2604.06514

Structure and unique factorization in concordance groups of links

Kouki Sato·Akira Yasuhara

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Abstract

Donald and Owens introduced two link concordance groups with a marked component and showed that they contain the knot concordance group as a direct summand with infinitely generated complements. While not explicitly posed by Donald and Owens, the problem of determining the structure of these complements arises naturally from their work. In this paper, we completely resolve this problem by proving that both complements are isomorphic to $\mathbb{Z}^{\infty} \oplus (\mathbb{Z}/2\mathbb{Z})^{\infty}$. Moreover, we introduce a notion of prime element and establish a unique prime decomposition theorem. This yields a canonical normal form, providing a complete description of the group structure.

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BibTeX RIS

Kouki Sato, Akira Yasuhara. 2026-04-07. Structure and unique factorization in concordance groups of links. https://arxiv.org/abs/2604.06514

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