Linking Number Obstructions To Satellite Homomorphisms

Document Type

Article

Publication Date

7-22-2024

Published In

Quantum Topology

Abstract

We prove that satellite operations that satisfy a certain positivity condition and have winding number other than one are not homomorphisms. The argument uses the d-invariants of branched covers. In the process, we prove a technical result relating d-invariants and the Torelli group which may be of independent interest.

Keywords

cyclic branched covers, Heegaard Floer homology, knot concordance group, satellite construction, Torelli group

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