On the nonexistence of a Green functor with values spinᶜ bordism and spin bordism

March 29, 2026Archiv der MathematikOpen Access

View Full Paper

Ask AI

Bookmark

Share

Key Points

The aim is to demonstrate that a specific C2-ring spectrum does not exist for spin^c bordism.
Analyzed the properties of C2-ring spectra and their fixed point spectra.
Examined the relationships between MSpin and MSpin^c in context of bordism theory.
Applied theoretical proofs to establish the nonexistence of the Green functor.
Proved that no C2-ring spectrum exists with MSpin^c as the underlying ring spectrum.
Demonstrated that Atiyah–Bott–Shapiro orientations cannot be derived from a single C2-ring spectrum.
Clarified the implications of this nonexistence for the study of bordism in algebraic topology.

Shows the nonexistence of a C2-ring spectrum for spin and spin^c bordism, indicating significant implications in algebraic topology.

No abstract yet. The journal hasn't published one we can show.

No takes yet. Share an insight, caveat, or question.

Abdallah et al. (2026) studied this question.

View Full Paper

Ask AI

Bookmark

Share