Rips Induction: Index of the dual lamination of an $\R$-tree

Mathematics – Group Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

33 pages. The previous version has been splitted in two disjoint papers. See also Botanic of irreducible automorphisms of free

Scientific paper

Let $T$ be a $\R$-tree in the boundary of the Outer Space CV$_N$, with dense orbits. The $Q$-index of $T$ is defined by means of the dual lamination of $T$. It is a generalisation of the Euler-Poincar\'e index of a foliation on a surface. We prove that the $Q$-index of $T$ is bounded above by $2N-2$, and we study the case of equality. The main tool is to develop the Rips Machine in order to deal with systems of isometries on compact $\R$-trees. Combining our results on the $\CQ$-index with results on the classical geometric index of a tree, we obtain a beginning of classification of trees. As a consequence, we give a classification of iwip outer automorphisms of the free group, by discussing the properties of their attracting and repelling trees.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Rips Induction: Index of the dual lamination of an $\R$-tree does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rips Induction: Index of the dual lamination of an $\R$-tree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rips Induction: Index of the dual lamination of an $\R$-tree will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-154883

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.