ترغب بنشر مسار تعليمي؟ اضغط هنا

Conjugation Curvature in Solvable Baumslag-Solitar Groups

162   0   0.0 ( 0 )
 نشر من قبل Alden Walker
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

We give a complete list of the cobounded actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces up to a natural equivalence relation. The set of equivalence classes carries a natural partial order first introduced by Abbott-Balasubra manya-Osin, and we describe the resulting poset completely. There are finitely many equivalence classes of actions, and each equivalence class contains the action on a point, a tree, or the hyperbolic plane.
We say that a group has property $R_{infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Felshtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{infty}$. We define a solvable generalization $Gamma(S)$ of these groups which we show to have property $R_{infty}$. We then show that property $R_{infty}$ is geometric for these groups, that is, any group quasi-isometric to $Gamma(S)$ has property $R_{infty}$ as well.
A generalized Baumslag-Solitar group is the fundamental group of a graph of groups all of whose vertex and edge groups are infinite cyclic. Levitt proves that any generalized Baumslag-Solitar group has property R-infinity, that is, any automorphism h as an infinite number of twisted conjugacy classes. We show that any group quasi-isometric to a generalized Baumslag-Solitar group also has property R-infinity. This extends work of the authors proving that any group quasi-isometric to a solvable Baumslag-Solitar BS(1,n) group has property R-infinity, and relies on the classification of generalized Baumslag-Solitar groups given by Whyte.
In this paper we classify Baumslag-Solitar groups up to commensurability. In order to prove our main result we give a solution to the isomorphism problem for a subclass of Generalised Baumslag-Solitar groups.
121 - Yves Stalder 2004
We study convergent sequences of Baumslag-Solitar groups in the space of marked groups. We prove that BS(m,n) --> F_2 for |m|,|n| --> infty and BS(1,n) --> Z wr Z for |n| --> infty. For m fixed, |m|>1, we show that the sequence (BS(m,n))_n is not con vergent and characterize many convergent subsequences. Moreover if X_m is the set of BS(m,n)s for n relatively prime to m and |n|>1, then the map BS(m,n) mapsto n extends continuously on the closure of X_m to a surjection onto invertible m-adic integers.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا