منابع مشابه
Quandles and Monodromy
We show that a variety of monodromy phenomena arising in geometric topology and algebraic geometry are most conveniently described in terms of homomorphisms from a(n augmented) knot quandle associated with the base to a suitable (augmented) quandle associated with the fiber. We consider the cases of the monodromy of a branched covering, braid monodromy and the monodromy of a Lefschetz fibration...
متن کاملAlexander Quandles of Order 16 *
Isomorphism classes of Alexander quandles of order 16 are determined, and classes of connected quandles are identified. This paper extends the list of known distinct connected finite Alexander quandles.
متن کاملClassification of Finite Alexander Quandles
Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t]-submodules Im(1 − t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Zn[t ]/(t − a) where gcd(n, a) = 1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. ...
متن کاملQuandles 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 knot quandle of the base as a manifold with a codimension 2 subspace (the set of singular values) ...
متن کاملSymbolic computation with finite quandles
Algorithms are described and Maple implementations are provided for finding all quandles of order n, as well as computing all homomorphisms between two finite quandles or from a finitely presented quandle (e.g., a knot quandle) to a finite quandle, computing the automorphism group of a finite quandle, etc. Several of these programs work for arbitrary binary operation tables and hence algebraic ...
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ژورنال
عنوان ژورنال: Algebra universalis
سال: 2017
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-017-0443-2