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# Mathematical Research Letters

## Volume 23 (2016)

### Number 4

### Yamabe invariants and the $\mathrm{Pin}^-(2)$-monopole equations

Pages: 1049 – 1069

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n4.a4

#### Authors

#### 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.

#### 2010 Mathematics Subject Classification

53C21, 53C25, 53C44, 57R57