The Outer Space of a Free Product

@inproceedings{Levitt2005TheOS,
  title={The Outer Space of a Free Product},
  author={Gilbert Levitt},
  year={2005}
}
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 dimension, or is VFL (it has a finite index subgroup with a finite classifying space), if the groups Gi… CONTINUE READING

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References

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Showing 1-10 of 23 references

Symmetric automorphisms of free products, Mem

  • D. McCullough, A. Miller
  • Amer. Math. Soc
  • 1996
Highly Influential
6 Excerpts

Moduli of graphs and automorphisms of free groups

  • M. Culler, K. Vogtmann
  • Invent. Math
  • 1986
Highly Influential
10 Excerpts

Limit groups and groups acting freely on R-trees

  • V. Guirardel
  • Geometry and Topology
  • 2004
3 Excerpts

Automorphisms of free groups and outer space, Geom. Dedic

  • K. Vogtmann
  • Caen Cedex, France. E-mail address: levitt@math…
  • 2002
1 Excerpt

Introduction to Λ-trees

  • I. Chiswell
  • World Scientific Publishing Co.,
  • 2001
1 Excerpt

The equivalence of some residual properties of word-hyperbolic groups

  • I. Kapovich, D. Wise
  • J. Algebra
  • 2000
1 Excerpt

Cut points and canonical splittings of hyperbolic groups

  • B. Bowditch
  • Acta Math
  • 1998
1 Excerpt

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