|
|||||
 |
|
|
|
|
|
New examples of
Brunnian theta graphs
Byoungwook Jang, Anna Kronaeur, Pratap Luitel, Daniel Medici, Scott A. Taylor and Alexander Zupan
Vol. 9 (2016), No. 5, 857–875
|
Abstract |
|
The Kinoshita graph is the most famous example of a Brunnian theta graph, a nontrivial spatial theta graph with the property that removing any edge yields an unknot. We produce a new family of diagrams of spatial theta graphs with the property that removing any edge results in the unknot. The family is parameterized by a certain subgroup of the pure braid group on four strands. We prove that infinitely many of these diagrams give rise to distinct Brunnian theta graphs. |
Keywords
spatial graph, almost unknotted graph, Brunnian, theta
graph, theta curve, rational tangle
|
Mathematical Subject Classification 2010
Primary: 57M25
|
Milestones
Received: 17 August 2015
Revised: 20 October 2015
Accepted: 22 October 2015
Published: 25 August 2016
Communicated by Joel Foisy
|
Authors |
| Byoungwook Jang | |
| Department of Mathematics and
Statistics Colby College c/o Scott Taylor Waterville, ME 04901-8858 United States |
|
| Anna Kronaeur | |
| Department of Mathematics and
Statistics Colby College Waterville, ME 04901-8858 United States |
|
| Pratap Luitel | |
| Department of Mathematics and
Statistics Colby College c/o Scott Taylor Waterville, ME 04901-8858 United States |
|
| Daniel Medici | |
| Department of Mathematics and
Statistics Colby College Waterville, ME 04901-8858 United States |
|
| Scott A. Taylor | |
| Department of Mathematics and
Statistics Colby College 5832 Mayflower Hill Waterville, ME 04901-8858 United States |
|
| Alexander Zupan | |
| Department of Mathematics University of Nebraska-Lincoln 1400 R Street Lincoln, NE 68588 United States |
|
|
