Khovanov homology and exotic surfaces in the 4-ball

Kyle Hayden, Isaac Sundberg

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show that the cobordism maps on Khovanov homology can distinguish smooth surfaces in the 4-ball that are exotically knotted (i.e., isotopic through ambient homeomorphisms but not ambient diffeomorphisms). We develop new techniques for distinguishing cobordism maps on Khovanov homology, drawing on knot symmetries and braid factorizations. We also show that Plamenevskaya’s transverse invariant in Khovanov homology is preserved by maps induced by positive ascending cobordisms.

Original languageEnglish (US)
Pages (from-to)217-246
Number of pages30
JournalJournal fur die Reine und Angewandte Mathematik
Volume2024
Issue number809
DOIs
StatePublished - Apr 1 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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