A partial resolution of Hedden’s conjecture on satellite homomorphisms

Key Points

• The result shows that specific patterns failing to exhibit homomorphism advances our understanding of knot theory.
• Proving that maps defined by even winding numbers do not form a homomorphism deepens the implications for smooth knot concordance.
• The exploration focuses on self-maps within the smooth knot concordance group to clarify Hedden's conjecture further.
• This finding may necessitate reevaluation of criteria for homomorphic behavior in satellite constructions.