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Symmetries of embedded complete bipartite graphs

Erica Flapan, Nicole Lehle, Blake Mellor, Matt Pittluck, Xan Vongsathorn (2014)

Fundamenta Mathematicae

We characterize which automorphisms of an arbitrary complete bipartite graph K n , m can be induced by a homeomorphism of some embedding of the graph in S³.

Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni, Kouki Taniyama (2009)

Fundamenta Mathematicae

An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the linking number of L is not congruent to 2 modulo 4. In this paper we study orientation-preserving or reversing symmetries of 2-component links, spatial complete graphs on 5 vertices and spatial complete bipartite graphs on 3 + 3 vertices in detail, and determine...

Systolic groups acting on complexes with no flats are word-hyperbolic

Piotr Przytycki (2007)

Fundamenta Mathematicae

We prove that if a group acts properly and cocompactly on a systolic complex, in whose 1-skeleton there is no isometrically embedded copy of the 1-skeleton of an equilaterally triangulated Euclidean plane, then the group is word-hyperbolic. This was conjectured by D. T. Wise.

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