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UNIFORM KAZHDAN CONSTANTS AND PARADOXES OF THE AFFINE PLANE
Journal article   Open access   Peer reviewed

UNIFORM KAZHDAN CONSTANTS AND PARADOXES OF THE AFFINE PLANE

Lam L Pham
Transformation groups, Vol.27(1), pp.239-269
03/01/2022
DOI: https://doi.org/10.1007/s00031-020-09600-5

Abstract

Science & Technology Mathematics Physical Sciences
LetG= SL(2,DOUBLE-STRUCK CAPITAL Z) & x22c9; DOUBLE-STRUCK CAPITAL Z(2)andH= SL(2,DOUBLE-STRUCK CAPITAL Z). We prove that the actionG & x21b7; Double-struck capital R(2)isuniformly non-amenableand that the quasi-regular representation ofGon l(2)(G/H) has auniform spectral gap. Both results are a consequence of a uniform quantitative form of ping-pong for affine transformations, which we establish here.
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https://doi.org/10.1007/s00031-020-09600-5View
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