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Certifying numerical estimates of spectral gaps

Certifying numerical estimates of spectral gaps AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Certifying numerical estimates of spectral gaps

Groups Complexity Cryptology , Volume 10 (1): 9 – May 1, 2018

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2018-0004
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Groups Complexity Cryptologyde Gruyter

Published: May 1, 2018

References