Connected sums and involutive knot Floer homology

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15 Scopus citations


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 languageEnglish (US)
Pages (from-to)214-265
Number of pages52
JournalProceedings of the London Mathematical Society
Issue number1
StatePublished - Jul 2019

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • 57M27
  • 57R56 (primary)


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