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ORBIFOLD LENS SPACES THAT ARE ISOSPECTRALBUT NOT ISOMETRIC

机译:等距而不是等距的奥宝镜头空间

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摘要

We answer Mark Kac's famous question [13], "can one hear the shape of a drum?" in the negative for orbifolds that are spherical space forms. This is done by extending the techniques developed by A. Ikeda on lens spaces to the orbifold setting. Several results are proved to show that with certain restrictions on the di-mensionalities of orbifold lens spaces we can obtain infinitely many pairs of iso-spectral non-isometric lens spaces. These results are then generalized to show that for any dimension greater than 8 we can have pairs of isospectral non-isometric orbi-fold lens spaces.
机译:我们回答马克·卡克(Mark Kac)的著名问题[13],“有人能听到鼓的声音吗?”在球面空间形式的球面的负数中。这是通过将A. Ikeda在镜头空间上开发的技术扩展到Orbifold设置来完成的。若干结果被证明表明,在对等倍透镜空间的尺寸进行一定限制的情况下,我们可以获得无限多对等光谱非等距透镜空间。然后将这些结果概括为表明,对于任何大于8的尺寸,我们都可以有成对的等光谱非等距双折透镜空间。

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