论文标题
广义的小取消条件，非阳性曲率和示意性降低性
Generalized small cancellation conditions, non-positive curvature and diagrammatic reducibility
论文作者
论文摘要
我们提出了一个度量条件$ {\ligalτ}'$，该$描述了经典小型取消组的几何形状，并也适用于其他已知类别的组（例如二维Artin组）。我们证明，满足条件$ {\ligalτ}'$的演示文稿在Sieradski和gersten的意义上是可降低的。特别是，我们推断出Artin组的标准呈现是非球面的，并且仅当它在图上可降低时。我们表明，在一些额外的假设下，$ {\grineτ}'$ - 组具有二次dehn函数和可解决的共轭问题。本着Greendlinger's Lemma的精神，我们证明，如果呈现$ p = \ langle x \ mid r \ mid r \ rangle $ of group $ g $的$ g $满足条件$ {\ lightτ}' - c'（\ frac {1} {1} {2} {2} {2}）$，则是$ x $的$ x $的$ x $的长度。 Relator。我们还引入了一个严格的度量条件$ {\grineτ}'_ {<} $，这意味着双曲线。最后，我们研究了这些条件的非计量和双重变体，并研究了小取消理论的谐波平均版本。
We present a metric condition ${\LARGEτ}'$ which describes the geometry of classical small cancellation groups and applies also to other known classes of groups such as two-dimensional Artin groups. We prove that presentations satisfying condition ${\LARGEτ}'$ are diagrammatically reducible in the sense of Sieradski and Gersten. In particular we deduce that the standard presentation of an Artin group is aspherical if and only if it is diagrammatically reducible. We show that, under some extra hypotheses, ${\LARGEτ}'$-groups have quadratic Dehn functions and solvable conjugacy problem. In the spirit of Greendlinger's lemma, we prove that if a presentation $P=\langle X \mid R\rangle$ of group $G$ satisfies conditions ${\LARGEτ}'-C'(\frac{1}{2})$, the length of any nontrivial word in the free group generated by $X$ representing the trivial element in $G$ is at least that of the shortest relator. We also introduce a strict metric condition ${\LARGEτ}'_{<}$, which implies hyperbolicity. Finally we investigate non-metric and dual variants of these conditions, and study a harmonic mean version of small cancellation theory.
