Quandles and Monodromy

Abstract

We show that a variety of monodromy phenomena arising in geometric topology and algebraic geometry are most conveniently described in terms of quandle homomorphisms from a knot quandle associated to the base to a quandle associated to a fiber. We consider the cases of the monodromy of a branched covering, braid monodromy and the monodromy of a Lefschetz fibration.

Much expanded version of math.GT/0201270, covering instances of monodromy beyond the monodromy of Lefschetz fibrations