Dissolving 4-manifolds, covering spaces and Yamabe invariant

Anar Akhmedov; Masashi Ishida; B. Doug Park

doi:10.1007/s10455-014-9445-x

Dissolving 4-manifolds, covering spaces and Yamabe invariant

Anar Akhmedov, Masashi Ishida, B. Doug Park

School of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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)
Pages (from-to)	271-283
Number of pages	13
Journal	Annals of Global Analysis and Geometry
Volume	47
Issue number	3
DOIs	https://doi.org/10.1007/s10455-014-9445-x
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

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10.1007/s10455-014-9445-x

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AU - Park, B. Doug

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N2 - 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.

AB - 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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KW - Dissolve

KW - Rosenberg conjecture

KW - Scalar curvature

KW - Yamabe invariant

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JO - Annals of Global Analysis and Geometry

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Dissolving 4-manifolds, covering spaces and Yamabe invariant

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