Yamabe Invariants and the ${\mathrm{Pin}}^{-}(2)$-monopole Equations

Abstract

We compute the Yamabe invariants for a new infinite class of closed $4$-dimensional manifolds by using a "twisted" version of the Seiberg-Witten equations, the ${\mathrm{Pin}}^{-}(2)$-monopole equations. The same technique also provides a new obstruction to the existence of Einstein metrics or long-time solutions of the normalised Ricci flow with uniformly bounded scalar curvature.

14 pages

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• ${\mathrm{Pin}}^{-}(2)$-monopole invariants