Abstract
Using cohomological methods, we show that lattices in semisimple groups are typically stable with respect to the Frobenius norm but not with respect to the operator norm.
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Acknowledgements
The authors wish to thank the referees who helped improving the paper in many places.
U. B. was partially supported by ISF Moked grant number 2919/19. A. L. acknowledges with gratitude the hospitality and support of the Fields Institute (Toronto) where part of thisworkwas carried out, aswell as a grant by the European Research Council (ERC) under the European Union’s Horizon 2020 (grant agreement No 882751). R.S. was partially supported by the projects 441426599 and 441848266 funded by the DFG (Deutsche Forschungsgemeinschaft). R. S. thanks the University of Chicago and the Weizmann Institute for hospitality when part of this workwas carried out. S.W. was partially supported by the NSF grant 2105451.
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Dedicated to Peter Sarnak with admiration and affection on the occasion of his 70th birthday
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Bader, U., Lubotzky, A., Sauer, R. et al. Stability and instability of lattices in semisimple groups. JAMA 151, 1–23 (2023). https://doi.org/10.1007/s11854-023-0329-5
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DOI: https://doi.org/10.1007/s11854-023-0329-5