اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe bounded Borel class and complex representations of 3-manifold groups
172
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
If $Gamma<mathrm{PSL}(2,mathbb{C})$ is a lattice, we define an invariant of a representation $Gammarightarrow mathrm{PSL}(n,mathbb{C})$ using the Borel class $beta(n)in mathrm{H}^3_mathrm{c}(mathrm{PSL}(n,mathbb{C}),mathbb{R})$. We show that the invariant is bounded and its maximal value is attained by conjugation of the composition of the lattice embedding with the irreducible complex representation $mathrm{PSL}(2,mathbb{C})rightarrow mathrm{PSL}(n,mathbb{C})$. Major ingredients of independent interest are the extension to degenerate configuration of flags of a Goncharov cocycle and its study, as well as the identification of $mathrm{H}^3_mathrm{c}(mathrm{SL}(n,mathbb{C}),mathbb{R})$ as a normed space.
قيم البحث
اقرأ أيضاً
We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3-manifolds and answer questions of Reid-Wang-Zhou and Agol-Liu.
We obtain infinitely many (non-conjugate) representations of 3-manifold fundamental groups into a lattice in the holomorphic isometry group of complex hyperbolic space. The lattice is an orbifold fundamental group of a branched covering of the projec
tive plane along an arrangement of hyperplanes constructed by Hirzebruch. The 3-manifolds are related to a Lefschetz fibration of the complex hyperbolic orbifold.
Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus. This
estimate is then used to deduce that mapping class groups are not uniformly perfect, and that the map from their second bounded cohomology to ordinary cohomology is not injective.
We study the TQFT mapping class group representations for surfaces with boundary associated with the $SU(2)$ gauge group, or equivalently the quantum group $U_q(Sl(2))$. We show that at a prime root of unity, these representations are all irreducible
. We also examine braid group representations for transcendental values of the quantum parameter, where we show that the image of every mapping class group is Zariski dense.
We prove that if the fundamental group of an arbitrary three-manifold -- not necessarily closed, nor orientable -- is a Kaehler group, then it is either finite or the fundamental group of a closed orientable surface.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
