Alexander-Conway invariants of tangles

Details Alexander-Conway invariants of tangles Alexander-Conway invariants of tangles

2010-11-29

arxiv.org/abs/1011.6200v1

Mathematics

Geometric Topology

14 pages, many figures

Scientific paper

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.

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