- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
2
2011
1
The Jones slopes of a knot
Stavros
Garoufalidis
Georgia Institute of Technology, ATLANTA, UNITED STATES
Knot, link, Jones polynomial, Jones slope, Jones period, quasi-polynomial, alternating knots, signature, pretzel knots, polytopes, Newton polygon, incompressible surfaces, slope, slope conjecture
The paper introduces the slope conjecture which relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. More precisely, we introduce two knot invariants, the Jones slopes (a finite set of rational numbers) and the Jones period (a natural number) of a knot in 3-space. We formulate a number of conjectures for these invariants and verify them by explicit computations for the class of alternating knots, the knots with at most 9 crossings, the torus knots and the (−2,3,n) pretzel knots.
Manifolds and cell complexes
General
43
69
10.4171/QT/13
http://www.ems-ph.org/doi/10.4171/QT/13