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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Deformations of Lie subgroups


Author: Don Coppersmith
Journal: Trans. Amer. Math. Soc. 233 (1977), 355-366
MSC: Primary 22E15
MathSciNet review: 0457621
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Abstract: We give rigidity and universality theorems for embedded deformations of Lie subgroups. If $ K \subset H \subset G$ are Lie groups, with $ {H^1}(K,g/h) = 0$, then for every $ {C^\infty }$ deformation of H, a conjugate of K lies in each nearby fiber $ {H_s}$. If $ H \subset G$ with $ {H^2}(H,g/h) = 0$, then there is a universal ``weak'' analytic deformation of H, whose base space is a manifold with tangent plane canonically identified with $ \operatorname{Ker} {\delta ^1}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0457621-1
PII: S 0002-9947(1977)0457621-1
Article copyright: © Copyright 1977 American Mathematical Society