ar X iv : 0 70 6 . 40 60 v 1 [ m at h . A G ] 2 7 Ju n 20 07 MINIMAL γ – SHEAVES MANUEL

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : 0 80 6 . 44 99 v 1 [ m at h . G N ] 2 7 Ju n 20 08 Aronszajn Compacta ∗

We consider a class of compacta X such that the maps from X onto metric compacta define an Aronszajn tree of closed subsets of X.

ar X iv : 0 70 4 . 17 02 v 3 [ m at h . A G ] 2 7 Ju n 20 08 THE CANONICAL VOLUME OF 3 - FOLDS OF GENERAL TYPE WITH χ ≤ 0

We prove that the canonical volume K ≥ 1 30 for all 3-folds of general type with χ(O) ≤ 0. This bound is sharp.

ar X iv : 0 70 4 . 17 02 v 2 [ m at h . A G ] 2 6 Ju n 20 08 THE CANONICAL VOLUME OF 3 - FOLDS OF GENERAL TYPE WITH χ ≤ 0

We prove that the canonical volume K ≥ 1 30 for all 3-folds of general type with χ(O) ≤ 0. This bound is sharp.

ar X iv : 0 70 7 . 09 70 v 2 [ m at h . G R ] 1 8 Ju l 2 00 7 Non - abelian free groups admit non - essentially free actions on rooted

We show that every finitely generated non-abelian free group Γ admits a spherically transitive action on a rooted tree T such that the action of Γ on the boundary of T is not essentially free. This reproves a result of Bergeron and Gaboriau. The existence of such an action answers a question of Grigorchuk, Nekrashevich and Sushchanskii.