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

Publisher Copyright:
© 2014, Springer Science+Business Media Dordrecht.

Keywords

4-manifold
Dissolve
Rosenberg conjecture
Scalar curvature
Yamabe invariant

Publisher link

10.1007/s10455-014-9445-x

Find It

Find It at U of M Libraries

Cite this

@article{0702a576e9844c6bb871183f432944e2,

title = "Dissolving 4-manifolds, covering spaces and Yamabe invariant",

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.",

keywords = "4-manifold, Dissolve, Rosenberg conjecture, Scalar curvature, Yamabe invariant",

author = "Anar Akhmedov and Masashi Ishida and Park, {B. Doug}",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media Dordrecht.",

year = "2015",

month = mar,

doi = "10.1007/s10455-014-9445-x",

language = "English (US)",

volume = "47",

pages = "271--283",

journal = "Annals of Global Analysis and Geometry",

issn = "0232-704X",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - Dissolving 4-manifolds, covering spaces and Yamabe invariant

AU - Akhmedov, Anar

AU - Ishida, Masashi

AU - Park, B. Doug

PY - 2015/3

Y1 - 2015/3

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.

KW - 4-manifold

KW - Dissolve

KW - Rosenberg conjecture

KW - Scalar curvature

KW - Yamabe invariant

UR - http://www.scopus.com/inward/record.url?scp=84925489634&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925489634&partnerID=8YFLogxK

U2 - 10.1007/s10455-014-9445-x

DO - 10.1007/s10455-014-9445-x

M3 - Article

AN - SCOPUS:84925489634

SN - 0232-704X

VL - 47

SP - 271

EP - 283

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 3

ER -

Dissolving 4-manifolds, covering spaces and Yamabe invariant

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this