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}
}
Comments
4 pages