Positive knots and knots with braid index three have property_p
William W. Menasco, Xingru Zhang
TL;DR
This paper proves that positive knots and knots with braid index three in the 3-sphere satisfy the Property P conjecture, advancing understanding of knot properties related to topology and knot invariants.
Contribution
It establishes the Property P conjecture for positive knots and knots with braid index three, which was previously unresolved.
Findings
Positive knots satisfy the Property P conjecture.
Knots with braid index three satisfy the Property P conjecture.
The result confirms the conjecture for a significant class of knots.
Abstract
We prove that positive knots and knots with braid index three in the 3-sphere satisfy the Property P conjecture.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models