5,937 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
Renormalization, isogenies and rational symmetries of differential equations
We give an example of infinite order rational transformation that leaves a
linear differential equation covariant. This example can be seen as a
non-trivial but still simple illustration of an exact representation of the
renormalization group.Comment: 36 page
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