ترغب بنشر مسار تعليمي؟ اضغط هنا

Surface groups in uniform lattices of some semi-simple groups

44   0   0.0 ( 0 )
 نشر من قبل Fran\\c{c}ois Labourie
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We show that uniform lattices in some semi-simple groups (notably complex ones) admit Anosov surface subgroups. This result has a quantitative version: we introduce a notion, called $K$-Sullivan maps, which generalizes the notion of $K$-quasi-circles in hyperbolic geometry, and show in particular that Sullivan maps are Holder. Using this notion, we show a quantitative version of our surface subgroup theorem and in particular that one can obtain $K$-Sullivan limit maps, as close as one wants to smooth round circles. All these results use the coarse geometry of path of triangles in a certain flag manifold and we prove an analogue to the Morse Lemma for quasi-geodesics in that context.



قيم البحث

اقرأ أيضاً

77 - E. Ebrahimi , S.M.B. Kashani , 2020
In this paper we investigate geodesic completeness of left-invariant Lorentzian metrics on a simple Lie group $G$ when there exists a left-invariant Killing vector field $Z$ on $G$. Among other results, it is proved that if $Z$ is timelike, or $G$ is strongly causal and $Z$ is lightlike, then the metric is complete. We then consider the special complex Lie group $SL_2(mathbb{C})$ in more details and show that the existence of a lightlike vector field $Z$ on it, implies geodesic completeness. We also consider the existence of a spacelike vector field $Z$ on $SL_2(mathbb{C})$ and provide an equivalent condition for the metric to be complete. This illustrates the complexity of the situation when $Z$ is spacelike.
We show that the group of almost automorphisms of a d-regular tree does not admit lattices. As far as we know this is the first such example among (compactly generated) simple locally compact groups.
The degree pattern of a finite group is the degree sequence of its prime graph in ascending order of vertices. We say that the problem of OD-characterization is solved for a finite group if we determine the number of pairwise nonisomorphic finite gro ups with the same order and degree pattern as the group under consideration. In this article the problem of OD-characterization is solved for some simple unitary groups. It was shown, in particular, that the simple unitary groups $U_3(q)$ and $U_4(q)$ are OD-characterizable, where $q$ is a prime power $<10^2$.
70 - Adrien Le Boudec 2020
We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of finitely gene rated simple groups quasi-isometric to a wreath product $C wr F$, where $C$ is a finite group and $F$ a non-abelian free group.
In arXiv:1802.02833 Guichard and Wienhard introduced the notion of $Theta$-positivity, a generalization of Lusztigs total positivity to real Lie groups that are not necessarily split. Based on this notion, we introduce in this paper $Theta$-positive representations of surface groups. We prove that $Theta$-positive representations are $Theta$-Anosov. This implies that $Theta$-positive representations are discrete and faithful and that the set of $Theta$-positive representations is open in the representation variety. We show that the set of $Theta$-positive representations is closed within the set of representations that do not virtually factor through a parabolic subgroup. From this we deduce that for any simple Lie group $mathsf G$ admitting a $Theta$-positive structure there exist components consisting of $Theta$-positive representations. More precisely we prove that the components parametrized using Higgs bundles methods in arXiv:2101.09377 consist of $Theta$-positive representations.
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