arXiv Open Access 2026

On the Non-Orientable $3$- and $4$-Genera of a Knot: Connections and Comparisons

Julia Knihs Jeanette Patel Joshua M. Sabloff Thea Rugg

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Abstrak

We define a new quantity, the Euler-normalized non-orientable genus, to connect a variety of ideas in the theory of non-orientable surfaces bounded by knots. This quantity is used to reframe non-orientable slice-torus bounds on the non-orientable $4$-genus, to bound below the Turaev genus as a measure of distance to an alternating knot, and to understand gaps between the $3$- and $4$-dimensional non-orientable genera of pretzel knots. Further, we make connections to essential surfaces in knot complements and the Slope Conjecture.

Topik & Kata Kunci

math.GT

Penulis (4)

Julia Knihs

Jeanette Patel

Joshua M. Sabloff

Thea Rugg

Format Sitasi

APA MLA BibTeX

Knihs, J., Patel, J., Sabloff, J.M., Rugg, T. (2026). On the Non-Orientable $3$- and $4$-Genera of a Knot: Connections and Comparisons. https://arxiv.org/abs/2602.13186

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2026
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓