ERRATUM TO REMARK 11.1 OF “FUKAYA CATEGORIES AND PICARD-LEFSCHETZ THEORY”

Abstract. We note an error in [1, Remark 11.1], pointed out by Zinger (who I would like to thank). This subject is discussed thoroughly in [2], but we provide a short summary here which focuses on the effect on [1]. The alternative sign convention suggested in [1, Remark 11.1] is incorrect, which means that it does not yield a topology on the determinant line bundle, as pointed out in [2, Remark 3.1]. In the general framework of [2], the intention of the Remark was to take the determinant line bundle as previously constructed in [1, Section 11a], and to pull back its topology by applying the discontinuous automorphism (−1)δ(δ−1)/2, where δ is the dimension of the cokernel of the Fredholm operator D. Applying these automrophisms changes the original isomorphism [1, Equation (11.2)] by (−1)δ1(δ1−2)/2+δ2(δ2−1)/2+(δ1+δ2)(δ1+δ2−1)/2 = (−1)δ1δ2, which yields (∧ i w∨1,i ∧