Elisenda Grigsby - Braids, complex geometry, and homology-type invariants

Описание: Elisenda Grigsby (Boston College)

Braids, complex geometry, and homology-type invariants

It's been known for a while that closed braids arise naturally when studying the vanishing sets of complex 2-variable polynomials. On the other hand, it should come as no surprise that not every closed braid arises in this way. Indeed, Lee Rudolph has given us a clean topological characterization of those that do: they are precisely the braids whose associated mapping classes satisfy a condition he calls quasipositivity. I'll remind you what this means, then tell you a few things (some old, some new) that the Khovanov-Lee homology of braid closures can tell us about quasipositivity.