论文标题
自由产品猫的外太空何时？
When is the Outer Space of a free product CAT(0)?
论文作者
论文摘要
guirardel和Levitt概括了Culler和Vogtmann的外层空间，为自由产品构建了一个外太空。我们完全表征了当这个空间（或真正的简单脊柱）支持均等的分段 - 欧几里德或分段hyperbolic cat（0）度量时。我们的结果主要是负面的，扩展了布里森的论文工作，并且与坎宁安的论文作品有关。特别是，只要脊柱的尺寸至少为三个，它绝不是猫（0）。令人惊讶的是，我们展示了一个自由产品系列，外太空是二维的，并且确实支持了一只epoiriant cat（0）度量。
Generalizing Culler and Vogtmann's Outer Space for the free group, Guirardel and Levitt construct an Outer Space for a free product of groups. We completely characterize when this space (or really its simplicial spine) supports an equivariant piecewise-Euclidean or piecewise-hyperbolic CAT(0) metric. Our results are mostly negative, extending thesis work of Bridson and related to thesis work of Cunningham. In particular, provided the dimension of the spine is at least three, it is never CAT(0). Surprisingly, we exhibit one family of free products for which the Outer Space is two-dimensional and does support an equivariant CAT(0) metric.
