Parameterized complexity of quantum knot invariants

International audienceWe give a general fixed parameter tractable algorithm to compute quantum invariants of links presented by diagrams, whose complexity is singly exponential in the carving-width (or the tree-width) of the diagram. In particular, we get a O(N^{3/2 cw} poly(n)) time algorithm to compute any Reshetikhin-Turaev invariant-derived from a simple Lie algebra g-of a link presented by a planar diagram with n crossings and carving-width cw, and whose components are coloured with g-modules of dimension at most N. For example, this includes the N th-coloured Jones polynomial and the N th-coloured HOMFLYPT polynomial