# The knots that lie above all shadows

## TL;DR

This paper classifies large reduced shadows in knot theory, showing they correspond to specific families of knots such as torus, twist, or connected sums of trefoils.

## Contribution

It provides a comprehensive classification of reduced shadows with many crossings, linking them to well-known knot types.

## Key findings

- Large reduced shadows are shadows of T(2,m+1), twist knots T_m, or sums of trefoil knots.
- The classification applies for all even integers m ≥ 2.
- This advances understanding of the relationship between shadows and knot types.

## Abstract

We show that for each even integer $m\ge 2$, every reduced shadow with sufficiently many crossings is a shadow of a torus knot T(2,m+1), or of a twist knot $T_m$, or of a connected sum of $m$ trefoil knots.