arXiv Open Access 2024

On the genera of symmetric unions of knots

Michel Boileau Teruaki Kitano Yuta Nozaki

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Abstrak

In the study of ribbon knots, Lamm introduced symmetric unions inspired by earlier work of Kinoshita and Terasaka. We show an identity between the twisted Alexander polynomials of a symmetric union and its partial knot. As a corollary, we obtain an inequality concerning their genera. It is known that there exists an epimorphism between their knot groups, and thus our inequality provides a positive answer to an old problem of Jonathan Simon in this case. Our formula also offers a useful condition to constrain possible symmetric union presentations of a given ribbon knot. It is an open question whether every ribbon knot is a symmetric union.

Topik & Kata Kunci

math.GT

Penulis (3)

Michel Boileau

Teruaki Kitano

Yuta Nozaki

Format Sitasi

APA MLA BibTeX

Boileau, M., Kitano, T., Nozaki, Y. (2024). On the genera of symmetric unions of knots. https://arxiv.org/abs/2407.09881

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓