330,668 research outputs found
Alexander-Conway invariants of tangles
We consider an algebra of (classical or virtual) tangles over an ordered
circuit operad and introduce Conway-type invariants of tangles which respect
this algebraic structure. The resulting invariants contain both the
coefficients of the Conway polynomial and the Milnor's mu-invariants of string
links as partial cases. The extension of the Conway polynomial to virtual
tangles satisfies the usual Conway skein relation and its coefficients are GPV
finite type invariants. As a by-product, we also obtain a simple representation
of the braid group which gives the Conway polynomial as a certain twisted
trace.Comment: 14 pages, many figure
Conway-Kochen and the Finite Precision Loophole
Recently Cator & Landsman made a comparison between Bell's Theorem and Conway
& Kochen's Strong Free Will Theorem. Their overall conclusion was that the
latter is stronger in that it uses fewer assumptions, but also that it has two
shortcomings. Firstly, no experimental test of the Conway-Kochen Theorem has
been performed thus far, and, secondly, because the Conway-Kochen Theorem is
strongly connected to the Kochen-Specker Theorem it may be susceptible to the
finite precision loophole of Meyer, Kent and Clifton. In this paper I show that
the finite precision loophole does not apply to the Conway-Kochen Theorem
A geometric construction of the Conway potential function
We give a geometric construction of the multivariable Conway potential
function for colored links. In the case of a single color, it is Kauffman's
definition of the Conway polynomial in terms of a Seifert matrix.Comment: 21 pages, 27 figure
A Factorization of the Conway Polynomial
A string link S can be closed in a canonical way to produce an ordinary
closed link L. We also consider a twisted closing which produces a knot K. We
give a formula for the Conway polynomial of L as a product of the Conway
polynomial of K times a power series whose coefficients are given as explicit
functions of the Milnor invariants of S. One consequence is a formula for the
first non-vanishing coefficient of the Conway polynomial of L in terms of the
Milnor invariants of L. There is an analogous factorization of the
multivariable Alexander polynomial.Comment: 20 pages, LaTeX, 9 figures using BoxedEP
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