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math.GT2012★ 1 cited
A state sum invariant of tangles in surfaces
Peter M. Johnson, Sóstenes Lins
In this paper we define a new state sum based on the regions defined by tangles on a surface which is an oriented closed surface with a finite number of open holes drilled. From th…
math.GT2012★ 2 cited
A graphical calculus for tangles in surfaces
Peter M. Johnson, Sóstenes Lins
We show how the theory of tangles is equivalent to that of well-connected tangles. These are drawn on a surface with boundary, and equivalent via Reidemeister moves of a restricted…