We construct new spin and nonspin 4-manifolds with zero signature that dissolve after a connected sum with only one copy of (Formula presented.). We use these 4-manifolds to construct new examples of 4-manifolds with negative Yamabe invariant and whose universal covers have positive Yamabe invariant. In particular, these provide new spin and nonspin counterexamples to a conjecture of Rosenberg in the case of dimension four.
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- Rosenberg conjecture
- Scalar curvature
- Yamabe invariant