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DISCONTINUOUS DUALITY THEOREM

TARO YOSHINO

Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku Kyoto, 606-8502, Japan

https://doi.org/10.1142/S0129167X07004370Cited by:2 (Source: Crossref)

Abstract

For a Lie group G and a subset H of G, Kobayashi [4] introduced the concept of the discontinuous dual of H as the set consisting of the subsets in G which are proper with H. Here, properness is a generalization of properly discontinuous actions. Kobayashi posed in the millenium volume [5] whether the discontinuous dual of H determines H uniquely up to a certain equivalence relation. In this paper, we solve this problem affirmatively.

Keywords:

AMSC: 22F30, 53C30

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