PIN(2)-monopole Floer homology and the Rokhlin invariant

Francesco Lin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We show that the bar version of the -monopole Floer homology of a three-manifold equipped with a self-conjugate spin structure is determined by the triple cup product of together with the Rokhlin invariants of the spin structures inducing . This is a manifestation of mod index theory and can be interpreted as a three-dimensional counterpart of Atiyah's classical results regarding spin structures on Riemann surfaces.

Original languageEnglish (US)
Pages (from-to)2681-2700
Number of pages20
JournalCompositio Mathematica
Issue number12
StatePublished - Dec 1 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Rokhlin invariant
  • monopole Floer homology
  • quaternionic operators


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