Parageometric outer automorphisms of free groups
Parageometric outer automorphisms of free groups
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自由群的参数外自同构
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
L. Mosher
中科院分区：
文献类型：
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作者：
M. Handel;L. Mosher
研究有限秩自由群Fr的全不可约外自同构o是parageometric的，这意味着o在外空间边界上的吸引不动点是关于Fr作用的几何R-树，但o本身不是几何外自同构，因为它不是曲面的同胚.我们的主要结果表明，o的展开因子严格大于o-1的展开因子。作为推论（由Guirardel独立证明），一个parageometric外自同构的逆既不是几何的也不是parageometric的，一个完全不可约的外自同构o是几何的当且仅当它在外空间边界上的吸引和排斥不动点是几何R-树。
We study those fully irreducible outer automorphisms o of a finite rank free group F r which are parageometric, meaning that the attracting fixed point of o in the boundary of outer space is a geometric R-tree with respect to the action of F r , but o itself is not a geometric outer automorphism in that it is not represented by a homeomorphism of a surface. Our main result shows that the expansion factor of o is strictly larger than the expansion factor of o -1 . As corollaries (proved independently by Guirardel), the inverse of a parageometric outer automorphism is neither geometric nor parageometric, and a fully irreducible outer automorphism o is geometric if and only if its attracting and repelling fixed points in the boundary of outer space are geometric R-trees.