arXiv Open Access 2025

Knots that share four surgeries

Marc Kegel Lisa Piccirillo

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Abstrak

Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct knots K,K' that have common Dehn surgeries for four distinct slopes. We also construct non-isotopic Legendrian knots K,K' that have contactomorphic contact (+1)-and (-1)-surgeries, disproving an analogous conjecture in contact geometry.

Topik & Kata Kunci

math.GT math.SG

Penulis (2)

Marc Kegel

Lisa Piccirillo

Format Sitasi

APA MLA BibTeX

Kegel, M., Piccirillo, L. (2025). Knots that share four surgeries. https://arxiv.org/abs/2505.13168

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓