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ON THE EXISTENCE OF A GLOBAL NEIGHBOURHOOD

Part of: Symplectic geometry, contact geometry Complex manifolds Projective and enumerative geometry

Published online by Cambridge University Press:  21 July 2015

TOM COATES  and
HIROSHI IRITANI
TOM COATES
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom e-mail: t.coates@imperial.ac.uk
HIROSHI IRITANI
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan e-mail: iritani@math.kyoto-u.ac.jp
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Abstract

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Suppose that a complex manifold M is locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, then they glue together to give a global neighbourhood of M. As an application, we prove a global version of Hertling–Manin's unfolding theorem for germs of TEP structures; this has applications in the study of quantum cohomology.

MSC classification

Primary: 32Q99: None of the above, but in this section
Secondary: 32Q40: Embedding theorems 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 717 - 726
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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