The outer space of a free product

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 Ja n 20 05 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 every Gi is Z, McCulloughMiller space when no Gi is Z. Our proof of contractibility 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 dimension, or is VFL (it has...

1 9 M ay 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...

On the Nilpotent Multiplier of a Free Product

determination of maximal singularity free zones in the workspace of parallel manipulator

due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singula...