We prove a formula for the conjugation action on the knot Floer complex of the connected sum of two knots. Using the formula we construct a homomorphism from the smooth concordance group to an abelian group consisting of chain complexes with homotopy automorphisms, modulo an equivalence relation. Using our connected sum formula, we perform some example computations of Hendricks and Manolescu's involutive invariants on large surgeries of connected sums of knots.
|Original language||English (US)|
|Number of pages||52|
|Journal||Proceedings of the London Mathematical Society|
|State||Published - Jul 2019|
All Science Journal Classification (ASJC) codes
- 57R56 (primary)