Orbit nonproper actions on Lorentz manifolds

Scott Adams

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 ∈ X, the orbit map g → gx : G → X is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G such that G admits a locally faithful, orbit nonproper action on a connected Lorentz manifold. In this paper, we describe three collections of groups such that G admits such an action iff G is in one of the three collections. In an earlier paper, we effectively described the first collection. In yet another paper, we describe effectively those groups in the second collection which are not contained in the union of the first and third. Finally, in another paper, we describe effectively the third collection.

Original languageEnglish (US)
Pages (from-to)201-243
Number of pages43
JournalGeometric and Functional Analysis
Volume11
Issue number2
DOIs
StatePublished - 2001

Bibliographical note

Funding Information:
The author was supported in part by NSF grant DMS-9703480.

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