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Some semigroups on a manifold with boundary


Author: T. H. McH. Hanson
Journal: Proc. Amer. Math. Soc. 25 (1970), 830-835
MSC: Primary 54.80; Secondary 22.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0263055-4
MathSciNet review: 0263055
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Abstract: In this paper, $ S$ is an abelian semigroup on an $ {\text{n}}$-dimensional simply connected manifold with boundary whose interior is a dense, simply connected, connected Lie group. We also assume there is a vector semigroup $ V_k^ - $ in $ S$ such that the interior of $ S$ misses the boundary of $ V_k^ - $, and such that $ (S - G{L_k})/{V_k}$ is a group. It is shown that if $ k = n$, then $ S$ is iseomorphic to $ V_n^ - $, and if $ k = 1,2$, or $ n - 1$, then $ S$ is iseomorphic to $ {V_{n - k}} \times V_k^ - $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0263055-4
Keywords: Simply connected manifold, boundary, vector semigroup, vector group, dimension, fundamental group, retract
Article copyright: © Copyright 1970 American Mathematical Society

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