اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConjugation Orbits of Loxodromic Pairs in SU(n,1)
73
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let ${bf H}_{mathbb C}^n$ be the $n$-dimensional complex hyperbolic space and ${rm SU}(n,1)$ be the (holomorphic) isometry group. An element $g$ in ${rm SU}(n,1)$ is called loxodromic or hyperbolic if it has exactly two fixed points on the boundary $partial {bf H}_{mathbb C}^n$. We classify ${rm SU}(n,1)$ conjugation orbits of pairs of loxodromic elements in ${rm SU}(n,1)$.
قيم البحث
اقرأ أيضاً
An infinite-type surface $Sigma$ is of type $mathcal{S}$ if it has an isolated puncture $p$ and admits shift maps. This includes all infinite-type surfaces with an isolated puncture outside of two sporadic classes. Given such a surface, we construct
an infinite family of intrinsically infinite-type mapping classes that act loxodromically on the relative arc graph $mathcal{A}(Sigma, p)$. J. Bavard produced such an element for the plane minus a Cantor set, and our result gives the first examples of such mapping classes for all other surfaces of type $mathcal{S}$. The elements we construct are the composition of three shift maps on $Sigma$, and we give an alternate characterization of these elements as a composition of a pseudo-Anosov on a finite-type subsurface of $Sigma$ and a standard shift map. We then explicitly find their limit points on the boundary of $mathcal{A}(Sigma,p)$ and their limiting geodesic laminations. Finally, we show that these infinite-type elements can be used to prove that Map$(Sigma,p)$ has an infinite-dimensional space of quasimorphisms.
Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3-manifolds, obtained by three different Dehn
surgeries on a fixed knot. In this paper, the behavior of $SU(N)$-instanton Floer homology with respect to Dehn surgery is studied. In particular, it is shown that there are surgery exact tetragons and pentagons, respectively, for $SU(3)$- and $SU(4)$-instanton Floer homologies. It is also conjectured that $SU(N)$-instanton Floer homology in general admits a surgery exact $(N+1)$-gon. An essential step in the proof is the construction of a family of asymptotically cylindrical metrics on ALE spaces of type $A_n$. This family is parametrized by the $(n-2)$-dimensional associahedron and consists of anti-self-dual metrics with positive scalar curvature. The metrics in the family also admit a torus symmetry.
This paper is devoted to the classification of GL^+(2,R)-orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of quadratic differentials. We show that the following dichotomy holds: an orbit is either closed
or dense in a connected component of the Prym eigenform locus. The proof uses several topological properties of Prym eigenforms, which are proved by the authors in a previous work. In particular the tools and the proof are independent of the recent results of Eskin-Mirzakhani-Mohammadi. As an application we obtain a finiteness result for the number of closed GL^+(2,R)-orbits (not necessarily primitive) in the Prym eigenform locus Prym_D(2,2) for any fixed D that is not a square.
We consider the highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory containing operators of the form tr(Z^{L-M} psi^M) where Z is a complex scalar and psi is a component of gaugino. We show that this state corresponds to the ope
rator tr(psi^L) and can be viewed as an analogue of the antiferromagnetic state in the su(2) sector. We find perturbative expansions of the energy of this state in both weak and strong t Hooft coupling regimes using asymptotic gauge theory Bethe ansatz equations. We also discuss a possible analog of this state in the conjectured string Bethe ansatz equations.
A pair $(alpha, beta)$ of simple closed geodesics on a closed and oriented hyperbolic surface $M_g$ of genus $g$ is called a filling pair if the complementary components of $alphacupbeta$ in $M_g$ are simply connected. The length of a filling pair is
defined to be the sum of their individual lengths. In cite{Aou}, Aougab-Huang conjectured that the length of any filling pair on $M$ is at least $frac{m_{g}}{2}$, where $m_{g}$ is the perimeter of the regular right-angled hyperbolic $left(8g-4right)$-gon. In this paper, we prove a generalized isoperimetric inequality for disconnected regions and we prove the Aougab-Huang conjecture as a corollary.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
