Topological Symmetry Groups of the Heawood Graph
We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in $S^3$.
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arXiv subjects
Robin T. Wilson
Publications and source records attributed to Robin T. Wilson.
The Structure of the Heawood Graph
We give a description of the cycle structure of the Heawood graph, $C_{14}$. In particular, we prove that the automorphism group of $C_{14}$ acts transitively on the set of $12$-cycles, Hamiltonian cycles, and disjoint pairs of $6$-cycles. We also enumerate $12$-, $10$-, and $8$-cycles in $C_{14}$, as well as pairs of disjoint $6$-cycles.
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Meridional Almost Normal Surfaces in Knot Complements
Suppose $K$ is a knot in a closed 3-manifold $M$ such that $\bar{M-N(K)}$ is irreducible. We show that for any positive integer $b$ there exists a triangulation of $\bar{M-N(K)}$ such that any weakly incompressible bridge surface for $K$ of $b$ bridges or fewer is isotopic to an almost normal bridge surface.
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Knots with infinitely many incompressible Seifert surfaces
We show that a knot in $S^3$ with an infinite number of distinct incompressible Seifert surfaces contains a closed incompressible surface in its complement.
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