Quandles and Lefschetz Fibrations
Geometric Topology
2007-05-23 v1
Abstract
We show that isotopy classes of simple closed curves in any oriented surface admit a quandle structure with operations induced by Dehn twists, the Dehn quandle of the surface. We further show that the monodromy of a Lefschetz fibration can be conveniently encoded as a quandle homomorphism from the knot quandle of the base as a manifold with a codimension 2 subspace (the set of singular values) to the Dehn quandle of the generic fibre, and discuss prospects for construction of invariants arising naturally from this description of the monodromy.
Cite
@article{arxiv.math/0201270,
title = {Quandles and Lefschetz Fibrations},
author = {D. N. Yetter},
journal= {arXiv preprint arXiv:math/0201270},
year = {2007}
}
Comments
10 pages