Tangles and generalizations of the Alexander polynomial
Seminar/Forum
In the study of lowdimensional topology, one of the classical link invariants is the Multivariable Alexander Polynomial, or MVA, originally defined by Torres. More recently, Archibald constructed a generalization to an invariant of virtual tangles, i.e. tangles in thickened surfaces rather than 3dimensional Euclidean space. This new invariant provides a straightforward verification of almost all the skein relations satisfied by the MVA. I will define a reduced version of Archibald’s invariant and discuss its relation to the Burau and Gassner representations for braids, as well as to BarNatan’s Alexandertype invariant of tangles without closed components.
Presenter

Dr Iva Halacheva, University of Melbourne