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DISCRETENESS BY USE OF A TEST MAP

Xi Fu|Liulan Li
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회보 (Bulletin of the KMS)|제49권 제1호|pp. 57-61

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참고문헌

키워드

discretenessnon-elementary Mobius grouptest map.
주제분류수학

초록

It is well known that one could use a fixed loxodromic or parabolic element of a non-elementary group $G{\subset}M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of G. In this paper, we show that a test map need not be in G. We also construct an example to show that the similar result using an elliptic element as a test map does not hold.

Abstract

It is well known that one could use a fixed loxodromic or parabolic element of a non-elementary group $G{\subset}M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of G. In this paper, we show that a test map need not be in G. We also construct an example to show that the similar result using an elliptic element as a test map does not hold.

참고문헌 (14)

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  8. X. Wang, "Discreteness criteria for Mobius groups acting on Rn", Israel J. Math, 150, pp.357~368 (2005)
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  10. X. Wang, "Dense subgroups and discrete subgroups in SL(2;C)", Quart. J. Math. Oxford Ser. (2), 50(200), pp.517~521 (1999)
  11. X. Wang, "Generating systems of subgroups in PSL(2;C)", Proc. Edinb. Math. Soc. (2), 45(1), pp.49~58 (2002)
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