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On Distortion Of Surface Groups In Right-Angled Artin Groups, Lucas Bridges
On Distortion Of Surface Groups In Right-Angled Artin Groups, Lucas Bridges
Mathematical Sciences Undergraduate Honors Theses
Surfaces have long been a topic of interest for scholars inside and outside of mathe- matics. In a topological sense, surfaces are spaces which appear flat on a local scale. Surfaces in this sense have a restricted set of properties, including the behavior of loops around a surface, codified in the fundamental group.
All but 3 surface groups have been shown to embed into a class of groups called right-angled Artin groups. The method through which these embeddings are created places large restrictions on all homomorphisms from surface groups to right-angled Artin groups.
One such restriction on these homomorphisms is …