Essays in Group Theory

Volume 8 of the series Mathematical Sciences Research Institute Publications pp 265-319

Dendrology of Groups: An Introduction

  • Peter B. ShalenAffiliated withUniversity of Illinois at Chicago

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The study of group actions on “generalized trees” or “ℝ-trees” has recently been attracting the attention of mathematicians in several different fields. This subject had its beginnings in the work of R. Lyndon [L] and I. Chiswell [Chi], and—from a different point of view—in the work of J. Tits [Ti]. The link between the points of view of these authors was provided by R. Alperin and K. Moss in [AM]. J. Morgan and I, in [MoS1,Mo2], established connections of this theory with hyperbolic geometry and with W. Thurston’s theory of measured laminations. The picture has been developed further by the above-mentioned people and also by H. Bass, M. Bestvina, M. Culler, H. Gillet, M. Gromov, W. Parry, F. Rimlinger and J. Stallings, among others.