Geodesic
Splittings and automorphisms of relatively hyperbolic groups
Vincent Guirardel1 ; Gilbert Levitt2
1Université de Rennes 1, Rennes, France
2Université de Caen Basse-Normandie, Caen, France
Groups, geometry, and dynamics, Tome 9 (2015) no. 2, pp. 599-663

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DOI

We study automorphisms of a relatively hyperbolic group G. When G is one-ended, we describe Out(G) using a preferred JSJ tree over subgroups that are virtually cyclic or parabolic. In particular, when G is toral relatively hyperbolic, Out(G) is virtually built out of mapping class groups and subgroups of GLn​(Z) fixing certain basis elements. When more general parabolic groups are allowed, these subgroups of GLn​(Z) have to be replaced by McCool groups: automorphisms of parabolic groups acting trivially (i.e. by conjugation) on certain subgroups.
DOI : 10.4171/ggd/322
Classification : 20-XX, 57-XX
Mots-clés : Groups of automorphisms, relatively hyperbolic group, splitting, hyperbolic group, groups acting on trees

Vincent Guirardel  1   ; Gilbert Levitt  2

1 Université de Rennes 1, Rennes, France
2 Université de Caen Basse-Normandie, Caen, France 
Vincent Guirardel; Gilbert Levitt. Splittings and automorphisms of relatively hyperbolic groups. Groups, geometry, and dynamics, Tome 9 (2015) no. 2, pp. 599-663. doi: 10.4171/ggd/322
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     year = {2015},
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     doi = {10.4171/ggd/322},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/322/}
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