English

Non injectivity of the "hair" map

Geometric Topology 2014-10-01 v3

Abstract

Kricker constructed a knot invariant Z^{rat} valued in a space of Feynman diagrams with beads. When composed with the so called "hair" map H, it gives the Kontsevich integral of the knot. We introduce a new grading on diagrams with beads and use it to show that a non trivial element constructed from Vogel's zero divisor in the algebra \Lambda\ is in the kernel of H. This shows that H is not injective.

Keywords

Cite

@article{arxiv.math/0202065,
  title  = {Non injectivity of the "hair" map},
  author = {Bertrand Patureau-Mirand},
  journal= {arXiv preprint arXiv:math/0202065},
  year   = {2014}
}

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4 pages