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Full-Text Articles in Other Mathematics
Bad Boundary Behavior In Star Invariant Subspaces I, William T. Ross, Andreas Hartmann
Bad Boundary Behavior In Star Invariant Subspaces I, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
We discuss the boundary behavior of functions in star invariant subspaces (BH2)1, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.
A Twisted Dimer Model For Knots, Heather M. Russell, Moshe Cohen, Oliver Dasbach
A Twisted Dimer Model For Knots, Heather M. Russell, Moshe Cohen, Oliver Dasbach
Department of Math & Statistics Faculty Publications
We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.
A Reduced Set Of Moves On One-Vertex Ribbon Graphs Coming From Links, Heather M. Russell, Susan Abernathy, Cody Armond, Moshe Cohen, Oliver T. Dasbach, Hannah Manuel, Chris Penn, Neal W. Stoltzfus
A Reduced Set Of Moves On One-Vertex Ribbon Graphs Coming From Links, Heather M. Russell, Susan Abernathy, Cody Armond, Moshe Cohen, Oliver T. Dasbach, Hannah Manuel, Chris Penn, Neal W. Stoltzfus
Department of Math & Statistics Faculty Publications
Every link in R3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.