46 research outputs found
Boundary slopes (nearly) bound cyclic slopes
Let r_m and r_M be the least and greatest finite boundary slopes of a
hyperbolic knot K in S^3. We show that any cyclic surgery slopes of K must lie
in the interval (r_m - 1/2, r_M + 1/2).Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-31.abs.htm
Intrinsically knotted graphs with 21 edges
We show that the 14 graphs obtained by moves on K_7
constitute a complete list of the minor minimal intrinsically knotted graphs on
21 edges. We also present evidence in support of a conjecture that the 20 graph
Heawood family, obtained by a combination of and
moves on K_7, is the list of graphs of size 21 that are
minor minimal with respect to the property not 2--apex.Comment: 21 pages, 11 figure