Positive Ricci Curvature on Highly Connected Manifolds

Diarmuid Crowley; David J.  Wraith

doi:10.4310/jdg/1497405625

Positive Ricci Curvature on Highly Connected Manifolds

Diarmuid Crowley, David J. Wraith

Mathematical Science

NATIONAL UNIVERSITY OF IRELAND

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

10 Citations (Scopus)

Abstract

For k ≥ 2, let M4k−1 be a closed (2k−2)-connected manifold. If k ≡ 1 mod 4 assume further that M is (2k−1)-parallelisable. Then there is a homotopy sphere Σ4k−1 such that M ]Σ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.

Original language	English
Pages (from-to)	187-243
Number of pages	57
Journal	Journal of Differential Geometry
Volume	106
Issue number	2
Early online date	14 Jun 2017
DOIs	https://doi.org/10.4310/jdg/1497405625
Publication status	Published - Jun 2017

Bibliographical note

Acknowledgments. We would like to thank Jim Davis, Anand Dessai,
Karsten Grove, Matthias Kreck, Gabriele Nebe, Walter Neumann,
Andrew Ranicki, Andras Stipsicz and Stephan Stolz for various helpful
comments. The first author would like to thank the National University
of Ireland Maynooth for its hospitality during the 2013 Irish Geometry
Conference, which directly supported research for this paper. The first
author acknowledges the support of the Leibniz Prize of Wolfgang Luck,
granted by the Deutsche Forschungsgemeinschaft.

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Cite this

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title = "Positive Ricci Curvature on Highly Connected Manifolds",

abstract = "For k ≥ 2, let M4k−1 be a closed (2k−2)-connected manifold. If k ≡ 1 mod 4 assume further that M is (2k−1)-parallelisable. Then there is a homotopy sphere Σ4k−1 such that M ]Σ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.",

author = "Diarmuid Crowley and Wraith, {David J.}",

note = "Acknowledgments. We would like to thank Jim Davis, Anand Dessai, Karsten Grove, Matthias Kreck, Gabriele Nebe, Walter Neumann, Andrew Ranicki, Andras Stipsicz and Stephan Stolz for various helpful comments. The first author would like to thank the National University of Ireland Maynooth for its hospitality during the 2013 Irish Geometry Conference, which directly supported research for this paper. The first author acknowledges the support of the Leibniz Prize of Wolfgang Luck, granted by the Deutsche Forschungsgemeinschaft.",

year = "2017",

month = jun,

doi = "10.4310/jdg/1497405625",

language = "English",

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T1 - Positive Ricci Curvature on Highly Connected Manifolds

AU - Crowley, Diarmuid

AU - Wraith, David J.

N1 - Acknowledgments. We would like to thank Jim Davis, Anand Dessai, Karsten Grove, Matthias Kreck, Gabriele Nebe, Walter Neumann, Andrew Ranicki, Andras Stipsicz and Stephan Stolz for various helpful comments. The first author would like to thank the National University of Ireland Maynooth for its hospitality during the 2013 Irish Geometry Conference, which directly supported research for this paper. The first author acknowledges the support of the Leibniz Prize of Wolfgang Luck, granted by the Deutsche Forschungsgemeinschaft.

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N2 - For k ≥ 2, let M4k−1 be a closed (2k−2)-connected manifold. If k ≡ 1 mod 4 assume further that M is (2k−1)-parallelisable. Then there is a homotopy sphere Σ4k−1 such that M ]Σ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.

AB - For k ≥ 2, let M4k−1 be a closed (2k−2)-connected manifold. If k ≡ 1 mod 4 assume further that M is (2k−1)-parallelisable. Then there is a homotopy sphere Σ4k−1 such that M ]Σ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.

U2 - 10.4310/jdg/1497405625

DO - 10.4310/jdg/1497405625

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VL - 106

SP - 187

EP - 243

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 2

ER -

Positive Ricci Curvature on Highly Connected Manifolds

Abstract

Bibliographical note

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