A PARTIAL ORDER ON THE SET OF PRIME KNOTS WITH UP TO 11 CROSSINGS

DOI10.1142/S0218216511008747zbMath1218.57004arXiv0906.3943MaRDI QIDQ5392878

Mineko Matsumoto, Keiichi Horie, Masaaki Suzuki, Teruaki Kitano

Publication date: 15 April 2011

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.3943

zbMATH Keywords

twisted Alexander polynomialsurjective homomorphismprime knot

Mathematics Subject Classification ID

Fundamental group, presentations, free differential calculus (57M05)

Related Items (9)

UPPER BOUNDS IN THE OHTSUKI–RILEY–SAKUMA PARTIAL ORDER ON 2-BRIDGE KNOTS ⋮ Epimorphisms between 2-bridge knot groups and their crossing numbers ⋮ An explicit relation between knot groups in lens spaces and those in S3 ⋮ On minimality of two-bridge knots ⋮ Introduction to twisted Alexander polynomials and related topics ⋮ Presentation length and Simon’s conjecture ⋮ Crosscap number and epimorphisms of two-bridge knot groups ⋮ Alexander invariants for virtual knots ⋮ Generating functions on epimorphisms between 2-bridge knot groups

Cites Work

• Unnamed Item
• Simon's conjecture for two-bridge knots
• A partial order in the knot table.II
• Ribbon concordance and a partial order on S-equivalence classes
• Ribbon concordance of knots in the 3-sphere
• Twisted Alexander polynomial for finitely presentable groups
• Twisted Alexander polynomials and surjectivity of a group homomorphism
• A Partial Order in the Knot Table
• CODING LINK DIAGRAMS
• Epimorphisms between 2-bridge link groups
• Twisted Alexander polynomials and a partial order on the set of prime knots
• Representations of knot groups and twisted Alexander polynomials

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