Geodesic
Zariski dense surface groups in SL(2k + 1, ℤ)
Long, D Darren 1   ; Thistlethwaite, Morwen B 2
1 Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States
2 Department of Mathematics, University of Tennessee, Knoxville, TN, United States
Geometry & topology, Tome 28 (2024) no. 3, pp. 1153-1166 Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We show that for all k, SL ⁡ (2k + 1, ℤ) contains surface groups which are Zariski dense in SL ⁡ (2k + 1, ℝ).

DOI : 10.2140/gt.2024.28.1153
Keywords: surface groups, integral representations, Hitchin component, Zariski dense

Long, D Darren  1   ; Thistlethwaite, Morwen B  2

1 Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States
2 Department of Mathematics, University of Tennessee, Knoxville, TN, United States 
@article{10_2140_gt_2024_28_1153,
     author = {Long, D Darren and Thistlethwaite, Morwen B},
     title = {Zariski dense surface groups in {SL(2k} + 1, {\ensuremath{\mathbb{Z}})}},
     journal = {Geometry & topology},
     pages = {1153--1166},
     year = {2024},
     volume = {28},
     number = {3},
     doi = {10.2140/gt.2024.28.1153},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2024.28.1153/}
}
TY  - JOUR
AU  - Long, D Darren
AU  - Thistlethwaite, Morwen B
TI  - Zariski dense surface groups in SL(2k + 1, ℤ)
JO  - Geometry & topology
PY  - 2024
SP  - 1153
EP  - 1166
VL  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2024.28.1153/
DO  - 10.2140/gt.2024.28.1153
ID  - 10_2140_gt_2024_28_1153
ER  - 
%0 Journal Article
%A Long, D Darren
%A Thistlethwaite, Morwen B
%T Zariski dense surface groups in SL(2k + 1, ℤ)
%J Geometry & topology
%D 2024
%P 1153-1166
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2024.28.1153/
%R 10.2140/gt.2024.28.1153
%F 10_2140_gt_2024_28_1153
Long, D Darren; Thistlethwaite, Morwen B. Zariski dense surface groups in SL(2k + 1, ℤ). Geometry & topology, Tome 28 (2024) no. 3, pp. 1153-1166. doi: 10.2140/gt.2024.28.1153

[1] D Alessandrini, G S Lee, F Schaffhauser, Hitchin components for orbifolds, J. Eur. Math. Soc. 25 (2023) 1285 | DOI

[2] H Bass, Groups of integral representation type, Pacific J. Math. 86 (1980) 15 | DOI

[3] J Bourgain, A Gamburd, P Sarnak, Affine linear sieve, expanders, and sum-product, Invent. Math. 179 (2010) 559 | DOI

[4] W J Culver, On the existence and uniqueness of the real logarithm of a matrix, Proc. Amer. Math. Soc. 17 (1966) 1146 | DOI

[5] O Guichard, Zariski closure of positive and maximal representations, in preparation

[6] F Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006) 51 | DOI

[7] D D Long, A W Reid, M Thistlethwaite, Zariski dense surface subgroups in SL(3, Z), Geom. Topol. 15 (2011) 1 | DOI

[8] D D Long, M B Thistlethwaite, Zariski dense surface subgroups in SL(4, Z), Exp. Math. 27 (2018) 82 | DOI

[9] D D Long, M Thistlethwaite, Zariski dense surface subgroups in SL(7, Z), computational output (2024)

[10] M V Nori, On subgroups of GLn(Fp), Invent. Math. 88 (1987) 257 | DOI

[11] P Sarnak, Notes on thin matrix groups, from: "Thin groups and superstrong approximation" (editors E Breuillard, H Oh), Math. Sci. Res. Inst. Publ. 61, Cambridge Univ. Press (2014) 343

[12] M Suzuki, Group theory, I, 247, Springer (1982)

[13] B Weisfeiler, Strong approximation for Zariski-dense subgroups of semisimple algebraic groups, Ann. of Math. 120 (1984) 271 | DOI

[14] M Zshornack, Integral Zariski dense surface groups in SL(n, R), preprint (2022)

Cité par Sources :