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Deformation spaces and normal forms around transversals

Abstract:

Given a manifold M with a submanifold N, the deformation space D(M, N) is a manifold with a submersion to R whose zero fiber is the normal bundle ν(M, N), and all other fibers are equal to M. This article uses deformation spaces to study the local behavior of various geometric structures associated with singular foliations, with N a submanifold transverse to the foliation. New examples include L∞-algebroids, Courant algebroids, and Lie bialgebroids. In each case, we obtain a normal form theor...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/S0010437X1900784X

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Exeter College
Role:
Author
Publisher:
Cambridge University Press Publisher's website
Journal:
Compositio Mathematica Journal website
Volume:
156
Issue:
4
Pages:
697-732
Publication date:
2020-02-17
Acceptance date:
2019-10-07
DOI:
EISSN:
1570-5846
ISSN:
0010-437X
Pubs id:
pubs:1081091
UUID:
uuid:06465883-403c-417e-b1a6-b8f17e6ec5d8
Source identifiers:
1081091
Local pid:
pubs:1081091

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