Abstract
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.
Original language | English (US) |
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Pages (from-to) | 271-283 |
Number of pages | 13 |
Journal | Annals of Global Analysis and Geometry |
Volume | 47 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2015 |
Bibliographical note
Funding Information:Anar Akhmedov was partially supported by NSF grant DMS-1005741. Masashi Ishida was partially supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 20540090. B. Doug Park was partially supported by an NSERC discovery grant.
Publisher Copyright:
© 2014, Springer Science+Business Media Dordrecht.
Keywords
- 4-manifold
- Dissolve
- Rosenberg conjecture
- Scalar curvature
- Yamabe invariant