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Organizers |
Dualities and Trialities from Ribbon Group Stabilizers
by
Lowell Abrams
George Washington University
Coauthors: Jo Ellis-Monaghan (Saint Michael's College)
The ribbon group acts on cellulary embedded graphs by applying Wilson operations, generated by dualizing and twisting, to individual edges. To account for actions on edge-labeled graphs, we reformulate this action in terms of a semidirect product with the symmetric group on the ribbons. In this context, we show how studying the stabilizers of single-vertex orientable embeddings provides an approach to produce, for example, self-dual and self-trial cellular embeddings that are not necessarily regular. We close with discussion of some results of a computer search for examples.
Date received: November 18, 2015
Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-34.