Abstract
We define the stabilizing number sn ( K ) of a knot K ⊂ S 3 as the minimal number n of S 2 × S 2 connected summands required for K to bound a null-homologous locally flat disk in D 4 # n S 2 × S 2 . This quantity is defined when the Arf invariant of K is zero. We show that sn ( K ) is bounded below by signatures and Casson–Gordon invariants and bounded above by the topological 4-genus g 4 top ( K ) . We provide an infinite family of examples with sn ( K ) < g 4 top ( K ) .
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