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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Rokhlin invariant
- monopole Floer homology
- quaternionic operators