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Dissolving 4-manifolds, covering spaces and Yamabe invariant

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Abstract

We construct new spin and nonspin 4-manifolds with zero signature that dissolve after a connected sum with only one copy of \(S^{2} \times S^{2}\). 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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Acknowledgments

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.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Anar Akhmedov

  2. Department of Mathematics, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

    Masashi Ishida

  3. Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    B. Doug Park

Authors
  1. Anar Akhmedov
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  2. Masashi Ishida
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  3. B. Doug Park
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Correspondence to B. Doug Park.

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Akhmedov, A., Ishida, M. & Park, B.D. Dissolving 4-manifolds, covering spaces and Yamabe invariant. Ann Glob Anal Geom 47, 271–283 (2015). https://doi.org/10.1007/s10455-014-9445-x

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  • DOI: https://doi.org/10.1007/s10455-014-9445-x

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