Unknotting number and L-space satellite operations

Abstract

We give a lower bound for the unknotting number under the L-space satellite operations. In the case of braided L-space satellite operations, including cabling operations, we obtain a stronger bound. The proof uses a lower bound for the unknotting number in knot Floer homology due to Alishahi-Eftekhary. The computational tool is a formula for computing the knot Floer complex under the L-space satellite operations, which was defined in the authors' previous work.

arXiv comment58 pages