Discrete circle actions: A note using non-standard analysis |
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| Authors: | Larry M Manevitz Shmuel Weinberger |
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| Institution: | (1) Department of Mathematics and Computer Science, Haifa University, Haifa, Israel;(2) Department of Computer Science, Polytechnic University, 11229 Brooklyn, New York, USA;(3) Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania, USA |
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| Abstract: | In this note we prove that the existence of effective uniformly Lipschitz ℚ/ℤ actions on manifolds (and other spaces) follows
from the existence of suchZ
nactions. The method of approach is non-standard analysis with all non-trivial transformation group theoretical information
concentrated in Newman's theorem; this results in a completely elementary argument. We give examples showing that, in contrast,
there are spaces with noS
1. effective actions despiteZ
nand hence ℚ/ℤ effective actions. |
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| Keywords: | |
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