Dehn surgeries on the figure eight knot: an upper bound for the complexity

TL;DR

This paper provides an upper bound on the complexity of manifolds resulting from p/q-surgeries on the figure eight knot, demonstrating sharpness for bounds up to 12.

Contribution

It introduces a specific upper bound for the complexity of manifolds from surgeries on the figure eight knot, with proven sharpness for certain values.

Findings

Upper bound $(p/q)$ for manifold complexity established

Bound is sharp when $(p/q)  12

Provides insights into the structure of manifolds from knot surgeries

Abstract

We establish an upper bound $\omega(p/q)$ on the complexity of manifolds obtained by $p/q$-surgeries on the figure eight knot. It turns out that if $\omega(p/q)\leqslant 12$, the bound is sharp.