Exact computation of the n-loop invariants of knots

Stavros Garoufalidis; Eric Sabo; Shane Scott

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arXiv · 1503.02554

Exact computation of the n-loop invariants of knots

Stavros Garoufalidis·Eric Sabo·Shane Scott

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Abstract

The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in $1/N$. We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power series of a knot. We give examples that illustrate our method and its results.

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Stavros Garoufalidis, Eric Sabo, Shane Scott. 2015-03-09. Exact computation of the n-loop invariants of knots. https://arxiv.org/abs/1503.02554

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