Multivariate Alexander quandles, IV. The medial quandle of a link
نویسندگان
چکیده
Joyce observed that the Alexander invariant and medial quandle of a classical knot are equivalent to each other, as invariants. In this paper, we discuss rather complicated extension Joyce’s observation several different quandles reduced (one-variable) modules associated with links. The theme is for links, provide stronger invariants than modules.
منابع مشابه
Alexander 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 کاملMatrices and finite Alexander quandles
We describe an algorithm for determining whether a finite quandle is isomorphic to an Alexander quandle by finding all possible Alexander presentations of the quandle. We give an implementation of this algorithm in Maple.
متن کاملPolynomial Cocycles of Alexander Quandles and Applications
Cocycles are constructed by polynomial expressions for Alexander quandles. As applications, non-triviality of some quandle homology groups are proved, and quandle cocycle invariants of knots are studied. In particular, for an infinite family of quandles, the non-triviality of quandle homology groups is proved for all odd dimensions.
متن کاملTopology Proceedings CLASSIFICATION 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. We...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2022
ISSN: ['1793-6527', '0218-2165']
DOI: https://doi.org/10.1142/s0218216522500778