Geometry & Topology: Damian Lin -- Virtual Knots and the Gordon-Litherland Linking Form

Monday 16 October 2023, 15:00-16:00, Carslaw 535 

Speaker: Damian Lin (Sydney) 

Title: Virtual Knots and the Gordon-Litherland Linking Form 

Abstract: We introduce virtual knots, a combinatorial generalisation of the
under-crossing and over-crossing information present in classical knot theory, that
aren’t subject to the same geometric restrictions.  There are also multiple different
geometric interpretations of virtual knots as knots on compact orientable surfaces.
Specific classes of virtual knots have nice properties, including the alternating
virtual knots, for which the Tait graph is well-defined.  This allows us to generalise a
powerful alternating knot invariant, able to distinguish the mutation classes of
alternating knots (Greene 2012).  This talk is based on joint work with Hans Boden,
Zsuzsanna Dancso and Tilda Wilkinson-Finch.