On the dimension datum of a subgroup and its application to isospectral manifolds

Jinpeng An Peking University Jiu-Kang Yu Purdue University Jun Yu ETH Zurich

Differential Geometry mathscidoc:1609.10308

Distinguished Paper Award in 2017

Journal of Differential Geometry, 94, (1), 59-85, 2013
The dimension datum of a subgroup of a compact Lie group is a piece of spectral information about that subgroup. We find some new invariants and phenomena of the dimension data and apply them to construct the first example of a pair of isospectral, simply connected closed Riemannian manifolds which are of different homotopy types. We also answer questions proposed by Langlands.
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@inproceedings{jinpeng2013on,
  title={ON THE DIMENSION DATUM OF A SUBGROUP AND ITS APPLICATION TO ISOSPECTRAL MANIFOLDS},
  author={Jinpeng An, Jiu-Kang Yu, and Jun Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074949972043970},
  booktitle={Journal of Differential Geometry},
  volume={94},
  number={1},
  pages={59-85},
  year={2013},
}
Jinpeng An, Jiu-Kang Yu, and Jun Yu. ON THE DIMENSION DATUM OF A SUBGROUP AND ITS APPLICATION TO ISOSPECTRAL MANIFOLDS. 2013. Vol. 94. In Journal of Differential Geometry. pp.59-85. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074949972043970.
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