Théorie des groupes
On the profinite rigidity of surface groups and surface words
Comptes Rendus. Mathématique, Tome 359 (2021) no. 2, pp. 119-122.

Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.121
Wilton, Henry 1

1 DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK.
@article{CRMATH_2021__359_2_119_0,
     author = {Wilton, Henry},
     title = {On the profinite rigidity of surface groups and surface words},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {119--122},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {2},
     year = {2021},
     doi = {10.5802/crmath.121},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.121/}
}
TY  - JOUR
AU  - Wilton, Henry
TI  - On the profinite rigidity of surface groups and surface words
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 119
EP  - 122
VL  - 359
IS  - 2
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.121/
DO  - 10.5802/crmath.121
LA  - en
ID  - CRMATH_2021__359_2_119_0
ER  - 
%0 Journal Article
%A Wilton, Henry
%T On the profinite rigidity of surface groups and surface words
%J Comptes Rendus. Mathématique
%D 2021
%P 119-122
%V 359
%N 2
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.121/
%R 10.5802/crmath.121
%G en
%F CRMATH_2021__359_2_119_0
Wilton, Henry. On the profinite rigidity of surface groups and surface words. Comptes Rendus. Mathématique, Tome 359 (2021) no. 2, pp. 119-122. doi : 10.5802/crmath.121. http://www.numdam.org/articles/10.5802/crmath.121/

[1] Baumslag, Benjamin Residually free groups, Proc. Lond. Math. Soc., Volume 17 (1967), pp. 402-418 | DOI | MR | Zbl

[2] Baumslag, Gilbert On generalised free product, Math. Z., Volume 78 (1962), pp. 423-438 | DOI | MR | Zbl

[3] Baumslag, Gilbert Residually finite groups with the same finite images, Compos. Math., Volume 29 (1974), pp. 249-252 | Numdam | MR | Zbl

[4] Bridson, Martin R.; McReynolds, David B.; Reid, Alan W.; Spitler, R. On the profinite rigidity of triangle groups (2004) (https://arxiv.org/abs/2004.07137)

[5] Bridson, Martin R.; McReynolds, David B.; Reid, Alan W.; Spitler, R. Absolute profinite rigidity and hyperbolic geometry, Ann. Math., Volume 192 (2020) no. 3, pp. 679-719 | DOI | MR | Zbl

[6] Grunewald, Fritz J.; Jaikin-Zapirain, Andrei; Zalesskii, Pavel A. Cohomological goodness and the profinite completion of Bianchi groups, Duke Math. J., Volume 144 (2008) no. 1, pp. 53-72 | DOI | MR | Zbl

[7] Hanany, Liam; Meiri, Chen; Puder, Doron Some orbits of free words that are determined by measures on finite groups, J. Algebra, Volume 555 (2020), pp. 305-324 | DOI | MR | Zbl

[8] Kharlampovich, Olga; Myasnikov, Alexei Irreducible affine varieties over a free group. I. Irreducibility of quadratic equations and Nullstellensatz, J. Algebra, Volume 200 (1998) no. 2, pp. 472-516 | DOI | MR | Zbl

[9] Magee, Michael; Puder, Doron Surface words are determined by word measures on groups (2019) (https://arxiv.org/pdf/1902.04873.pdf, to appear in Israel Journal of Mathematics)

[10] Noskov, Guennadi A.; Remeslennikov, Vladimir N.; Roman’kov, Vitaly A. Infinite groups, Itogi Nauki Tekh., Ser. Algebra, Topologiya, Geom., Volume 17 (1979), pp. 65-157 | Zbl

[11] Puder, Doron; Parzanchevski, Ori Measure preserving words are primitive, J. Am. Math. Soc., Volume 28 (2015) no. 1, pp. 63-97 | DOI | MR | Zbl

[12] Sela, Zlil Diophantine geometry over groups. I. Makanin–Razborov diagrams, Publ. Math., Inst. Hautes Étud. Sci., Volume 93 (2001), pp. 31-105 | DOI | Numdam | MR | Zbl

[13] Serre, Jean-Pierre Galois cohomology, Springer Monographs in Mathematics, Springer, 1997 (Translated from the French by Patrick Ion and revised by the author) | Zbl

[14] Wilton, Henry Hall’s Theorem for limit groups, Geom. Funct. Anal., Volume 18 (2008) no. 1, pp. 271-303 | DOI | MR | Zbl

[15] Wilton, Henry Essential surfaces in graph pairs, J. Am. Math. Soc., Volume 31 (2018) no. 4, pp. 893-919 | DOI | MR | Zbl

[16] Wilton, Henry; Zalesskii, Pavel Distinguishing geometries using finite quotients, Geom. Topol., Volume 21 (2017) no. 1, pp. 345-384 | DOI | MR | Zbl

[17] Wilton, Henry; Zalesskii, Pavel A. Profinite detection of 3-manifold decompositions, Compos. Math., Volume 155 (2019) no. 2, pp. 246-259 | DOI | MR | Zbl

[18] Wise, Daniel T. Subgroup separability of graphs of free groups with cyclic edge groups, Q. J. Math, Volume 51 (2000) no. 1, pp. 107-129 | DOI | MR | Zbl

Cité par Sources :