An odd Khovanov homotopy type

Sucharit Sarkar, Christopher Scaduto, Matthew Stoffregen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

For each link L⊂S3 and every quantum grading j, we construct a stable homotopy type Xo j(L) whose cohomology recovers Ozsváth-Rasmussen-Szabó's odd Khovanov homology, H˜i(Xo j(L))=Kho i,j(L), following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable homotopy type. Furthermore, the odd Khovanov homotopy type carries a Z/2 action whose fixed point set is a desuspension of the even Khovanov homotopy type. We also construct a potentially new even Khovanov homotopy type with a Z/2 action, with fixed point set a desuspension of Xo j(L).

Original languageEnglish (US)
Article number107112
JournalAdvances in Mathematics
Volume367
DOIs
StatePublished - Jun 24 2020
Externally publishedYes

Keywords

  • Odd Khovanov homology
  • Stable homotopy refinement

ASJC Scopus subject areas

  • Mathematics(all)

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