论文标题
可解决的Baumslag-Solitar群体中的共轭曲率
Conjugation Curvature in Solvable Baumslag-Solitar Groups
论文作者
论文摘要
对于$ bs（1，n）= \ langle t，a |中的元素tat^{ - 1} = a^n \ rangle $以普通形式写成$ t^{ - u} a^vt^w $，带有$ u，w \ geq 0 $和$ v \ in \ mathbb {z} $，我们展示了代表元素的地理位词，代表元素的词长度，并给出了$ a $ a \ a \ a \ a的词长度。使用此单词长度公式，我们证明了由Bar Natan，Duchin和Kropholler定义的正密度的一组元素。
For an element in $BS(1,n) = \langle t,a | tat^{-1} = a^n \rangle$ written in the normal form $t^{-u}a^vt^w$ with $u,w \geq 0$ and $v \in \mathbb{Z}$, we exhibit a geodesic word representing the element and give a formula for its word length with respect to the generating set $\{t,a\}$. Using this word length formula, we prove that there are sets of elements of positive density of positive, negative and zero conjugation curvature, as defined by Bar Natan, Duchin and Kropholler.
