Abstract
We establish a lower bound on the spectral gap of the Laplace operator on special linear groups using conic optimisation. In particular, this provides a constructive (but computer assisted) proof that these groups have the Kazhdan property (T). Software for such optimisation for other finitely presented groups is provided.
Funding source: Narodowe Centrum Nauki
Award Identifier / Grant number: 2015/19/B/ST1/01458
Funding source: H2020 European Research Council
Award Identifier / Grant number: 677120-INDEX
Funding statement: The first author has been partially supported by the National Science Centre, under grant number 2015/19/B/ST1/01458. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 677120-INDEX).
Acknowledgements
We would like to thank Dawid Kielak and Taka Ozawa for valuable comments.
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