1 9 M ay 2 00 6 THE OUTER SPACE OF A FREE PRODUCT

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

2 9 A ug 2 00 6 THE OUTER SPACE OF A FREE PRODUCT

We associate a contractible “outer space” to any free product of groups G = G1 ∗ · · · ∗ Gq. It equals Culler-Vogtmann space when G is free, McCulloughMiller space when no Gi is Z. Our proof of contractibility (given when G is not free) is based on Skora’s idea of deforming morphisms between trees. Using the action of Out(G) on this space, we show that Out(G) has finite virtual cohomological di...

1 9 M ay 2 00 6 DEFORMATION SPACES OF TREES

Let G be a finitely generated group. Two simplicial G-trees are said to be in the same deformation space if they have the same elliptic subgroups (if H fixes a point in one tree, it also does in the other). Examples include Culler-Vogtmann’s outer space, and spaces of JSJ decompositions. We discuss what features are common to trees in a given deformation space, how to pass from one tree to all ...

1 9 M ay 2 00 2 Electronic states in ideal free standing films

ua nt - p h / 06 05 21 9 v 1 2 5 M ay 2 00 6 Classical simulators of quantum computers and no - go theorems

It is discussed, why classical simulators of quantum computers escape from some no-go claims like Kochen-Specker, Bell, or recent Conway-Kochen " Free Will " theorems.