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A Kontsevich integral of order 1. (arXiv:1810.05747v1 [math.GT])
来源于:arXiv
We define a 1-cocycle in the space of long knots that is a natural
generalisation of the Kontsevich integral seen as a 0-cocycle. It involves a
2-form that generalises the Knizhnik--Zamolodchikov connection. Similarly to
the Kontsevich integral, it lives in a space of chord diagrams of the same kind
as those that make the principal parts of Vassiliev's 1-cocycles. Moreover, up
to a change of variable similar to the one that led Birman--Lin to discover the
4T relations, we show that the relations defining our space, which allow the
integral to be finite and invariant, are dual to the maps that define
Vassiliev's cohomology in degree 1. 查看全文>>