Surface subgroups of Kleinian groups with torsion

Homéomorphismes et nombre d'intersection

“…Therefore we have only to consider hyperbolic 3-manfolds. The conjecture was proved in the case of arithmetic hyperbolic manifolds by Lackenby [122], and was solved in general form by Kahn and Markovic [116]. Conjectures (2) and (4) (and hence also (3)) were solved by Agol, assuming the result of Kahn-Markovic, after partial results of Cooper-Long-Reid [61] and Bergeron-Wise [25] among others.…”

Free groups in lattices

“…This theorem now follows from Theorem 1.4. Theorem 1.4 plays a key role in the two recent papers by Lackenby, Long and Reid [11] and Lackenby [10]. The first relates LERF with the Lubotzky-Sarnak conjecture and the second proves that Kleinian groups that contain noncyclic finite subgroups are either virtually free or contain a surface subgroup.…”

A Glimpse into Thurston’s Work

“…Therefore we have only to consider hyperbolic 3-manfolds. The conjecture was proved in the case of arithmetic hyperbolic manifolds by Lackenby [122], and was solved in general form by Kahn and Markovic [116]. Conjectures (2) and (4) (and hence also (3)) were solved by Agol, assuming the result of Kahn-Markovic, after partial results of Cooper-Long-Reid [61] and Bergeron-Wise [25] among others.…”