The Magnus Representation for the Group of Homology Cylinders
نویسندگان
چکیده
We define and study the Magnus representation for homology cylinders generalizing the work of Kirk, Livingston and Wang [KLW] which treats the case of string links. Using this, we give a factorization formula of Alexander polynomials for three dimensional manifolds obtained by closing homology cylinders. We also show a relationship between the Gassner representation for string links and the Magnus representation for homology cylinders.
منابع مشابه
The Magnus Representation for Homology Cylinders
We study the Magnus representation for homology cylinders as a generalization of the Gassner representation for string links defined by Le Dimet [12] and Kirk-Livingston-Wang [11]. As an application, we give some factorization formulas of higher-order degree invariants defined by Harvey in [9], [10] for closed three dimensional manifolds obtained from homology cylinders.
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