TL;DR
This paper establishes a lower bound on the crossing number of satellite knots relative to their companion knots, providing a quantitative relationship between their complexities.
Contribution
It introduces a novel inequality linking satellite knot crossing numbers to those of their companions, advancing understanding of knot complexity relationships.
Findings
Crossing number of satellite knots is at least 10^{-13} times that of the companion.
Provides a quantitative lower bound relating satellite and companion knot complexities.
Enhances theoretical understanding of knot crossing number relationships.
Abstract
We show that the crossing number of a satellite knot is at least 10^{-13} times the crossing number of its companion knot.
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