Transitive Actions on Lorentz Manifolds with Noncompact Stabilizer |
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Authors: | Scot Adams |
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Institution: | (1) School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, U.S.A. |
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Abstract: | If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some x![thinsp](/content/m618355163007672/xxlarge8201.gif) ![isin](/content/m618355163007672/xxlarge8712.gif) X, the orbit map g gx:G![thinsp](/content/m618355163007672/xxlarge8201.gif) ![rarr](/content/m618355163007672/xxlarge8594.gif) X is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G admitting a locally faithful, orbit nonproper, isometric action on a connected Lorentz manifold. In an earlier paper, we found three collections of groups such that G admits such an action iff G is in one of the three collections. In another paper, we effectively described the first collection. In this paper, we show that the second collection contains a small, effectively described collection of groups, and, aside from those, it is contained in the union of the first and third collections. Finally, in a third paper, we effectively describe the third collection, thus solving the stated problem. |
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Keywords: | isometries Lorentz manifolds transformation groups |
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