3-Manifold Seminar: Diagrams on surfaces and an invariant of virtual spatial graphs

Seminar | April 17 | 12:40-2 p.m. | 891 Evans Hall

 Kyle Miller, UC Berkeley

 Department of Mathematics

Knots and spatial graphs can be represented as diagrams, which are planar graphs with special $4$-valent vertices for the crossings. Kauffman proposed considering diagrams on non-planar surfaces as well, and the corresponding objects are called virtual knots and virtual spatial graphs. In this talk, I will describe the Brauer category (a Tempereley-Lieb-like category for diagrams on surfaces), an extension of the flow polynomial to surface graphs, and an extension of the Yamada polynomial to virtual spatial graphs. Combined with another extension of the Yamada polynomial by Fleming and Mellor, I will describe a partial test for whether a virtual spatial graph is not virtually equivalent to a spatial graph.

This is joint work with Calvin McPhail-Snyder.