A minimality property for knots without Khovanov 2-torsion

A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology.We show that if a knot K has no 2-torsion in its Khovanov homology, then the rank of its reduced Khovanov homology is minimal among all knots obtainable from K by a proper rational tangle replacement.It follows, for example, that unknotting number 1 knots have 2-torsion in their Khovanov homology. 57K18Shumakovitch conjectured that every nontrivial knot has an element of order 2 in its Khovanov homology [10, Conjecture 1].The conjecture has been verified for some infinite families of knots (see, for example, [2; 9; 10]) and has withstood large computational searches.In this note, we provide topological evidence for the conjecture, and we verify the conjecture for a large class of knots that include all unknotting number 1 knots.