We give simple examples of finitely presented Kazhdan groups with infinite outer automorphism groups, as arithmetic lattices in Lie groups. This answers a question of Paulin, independently answered by Ollivier and Wise by completely different methods. We also use results of Abels about compact presentability of p-adic groups to exhibit a finitely presented non-Hopfian Kazhdan group. This answer...

We give simple examples of finitely presented Kazhdan groups with infinite outer automorphism groups, as arithmetic lattices in Lie groups. This answers a question of Paulin, independently answered by Ollivier and Wise by completely different methods. We also use results of Abels about compact presentability of p-adic groups to exhibit a finitely presented non-Hopfian Kazhdan group. This answer...

This is the second in a series of papers about torsionfree groups which act properly and cocompactly on a CAT(0) metric space with isolated flats and relatively thin triangles. Our approach is to adapt the methods of Sela and others for wordhyperbolic groups to this context of non-positive curvature. The main result in this paper is that (under certain technical hypotheses) such a group as abov...

Let B n be the braid group on n 4 strands. We prove that B n modulo its center is co-Hoppan. We then show that any injective endomorphism of B n is geometric in the sense that it is induced by a homeomorphism of a punctured disk. We further prove that any injection from B n to B n+1 is geometric for n 7. Additionally, we obtain analogous results for mapping class groups of punctured spheres. Th...

We apply the method of Arzhantseva-Ol’shanskii to prove that for an exponentially generic (in the sense of Ol’shanskii) class of one-relator groups the isomorphism problem is solvable in at most exponential time. This is obtained as a corollary of the more general result that for any fixed integers m > 1, n > 0 there is an exponentially generic class of m-generator n-relator groups where every ...