Quandles and Lefschetz Fibrations

Quandles and Lefschetz Fibrations

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 k...

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Bibliographic Details
Main Author: Yetter, D. N
Format: Journal Article
Language:English
Published: 28-01-2002
Subjects:
Mathematics - Geometric Topology
Online Access:Get full text
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Summary: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.
DOI:10.48550/arxiv.math/0201270