Milnor invariants of string links, trivalent trees, and configuration space integrals
Abstract
We study configuration space integral formulas for Milnor's homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a certain space of trivalent "homotopy link diagrams" which corresponds to all finite type homotopy link invariants via configuration space integrals. An important ingredient is the fact that configuration space integrals take the shuffle product of diagrams to the product of invariants. We ultimately deduce a partial recipe for writing explicit integral formulas for products of Milnor invariants from trivalent forests. We also obtain cohomology classes in spaces of link maps from the same data.
Keywords
Cite
@article{arxiv.1511.02768,
title = {Milnor invariants of string links, trivalent trees, and configuration space integrals},
author = {Robin Koytcheff and Ismar Volic},
journal= {arXiv preprint arXiv:1511.02768},
year = {2021}
}
Comments
Changes from last version: removed odd parity assumption in result on classes in higher-dimensional spaces of link maps; other minor revisions. 23 pages. Accepted for publication in Topology Appl