On the spectral gap for finitely-generated subgroups of SU(2)

被引：85

作者：

Bourgain, Jean ^{[1
]}

Gamburd, Alex

机构：

[1] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

[2] Univ Calif Santa Cruz, Sch Math, Inst Adv Study, Santa Cruz, CA 95064 USA

[3] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

INVENTIONES MATHEMATICAE | 2008年 / 171卷 / 01期

关键词：

D O I：

10.1007/s00222-007-0072-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the spectral gap property for free subgroups of SU(2) generated by elements satisfying a noncommutative diophantine property, in particular for free subgroups generated by elements with algebraic entries.

引用

页码：83 / 121

页数：39

共 31 条

[1] [Anonymous], 1923, FUND MATH, DOI DOI 10.4064/FM-4-1-7-33
[2] A sum-product estimate in finite fields, and applications
Bourgain, J
Katz, N
Tao, T
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2004, 14 (01) : 27 - 57
[3] On the Erdos-Volkmann and Katz-Tao ring conjectures
Bourgain, J
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2003, 13 (02) : 334 - 365
[4] Quaquaversal tilings and rotations
Conway, JH
Radin, C
[J]. INVENTIONES MATHEMATICAE, 1998, 132 (01) : 179 - 188
[5] Dawson CM, 2006, QUANTUM INFORM COMPU, V6, P81
[6] DELAHARPE P, 1983, ENSEIGN MATH, V29, P129
[7] Draco B, 2000, DISCRETE COMPUT GEOM, V23, P419, DOI 10.1007/s004540010009
[8] DRINFELD VG, 1984, FUNCT ANAL APPL+, V18, P245
[9] ALMOST ALL SUBGROUPS OF A LIE GROUP ARE FREE
EPSTEIN, DBA
[J]. JOURNAL OF ALGEBRA, 1971, 19 (02) : 261 - &
[10] Fisher D, 2006, INT MATH RES NOTICES, V2006

← 1 2 3 4 →