Deformations of asymptotically cylindrical G2-manifolds

Johannes Nordström

doi:10.1017/S0305004108001333

Deformations of asymptotically cylindrical G₂-manifolds

Johannes Nordström

Department of Mathematical Sciences

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

14 Citations (SciVal)

Abstract

We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G₂-structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically cylindrical G₂-manifold is exactly G₂ if and only if the fundamental group π₁(M) is finite and neither M nor any double cover of M is homeomorphic to a cylinder.

Original language	English
Pages (from-to)	311-348
Number of pages	38
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	145
Issue number	2
Early online date	19 May 2008
DOIs	https://doi.org/10.1017/S0305004108001333
Publication status	Published - 1 Sept 2008

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AB - We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G2-structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically cylindrical G2-manifold is exactly G2 if and only if the fundamental group π1(M) is finite and neither M nor any double cover of M is homeomorphic to a cylinder.

UR - https://www.scopus.com/pages/publications/49549106009

UR - http://dx.doi.org/10.1017/S0305004108001333

U2 - 10.1017/S0305004108001333

DO - 10.1017/S0305004108001333

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SP - 311

EP - 348

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

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Deformations of asymptotically cylindrical G₂-manifolds

Abstract

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