New examples of Brunnian theta graphs
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 nonisotopic Brunnian theta graphs.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.03014
 Bibcode:
 2015arXiv150803014J
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 Accepted by Involve