اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the mod-$ell$ homology of the classifying space for commutativity
99
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the mod-$ell$ homotopy type of classifying spaces for commutativity, $B(mathbb{Z}, G)$, at a prime $ell$. We show that the mod-$ell$ homology of $B(mathbb{Z}, G)$ depends on the mod-$ell$ homotopy type of $BG$ when $G$ is a compact connected Lie group, in the sense that a mod-$ell$ homology isomorphism $BG to BH$ for such groups induces a mod-$ell$ homology isomorphism $B(mathbb{Z}, G) to B(mathbb{Z}, H)$. In order to prove this result, we study a presentation of $B(mathbb{Z}, G)$ as a homotopy colimit over a topological poset of closed abelian subgroups, expanding on an idea of Adem and Gomez. We also study the relationship between the mod-$ell$ type of a Lie group $G(mathbb{C})$ and the locally finite group $G(bar{mathbb{F}}_p)$ where $G$ is a Chevalley group. We see that the naive analogue for $B(mathbb{Z}, G)$ of the celebrated Friedlander--Mislin result cannot hold, but we show that it does hold after taking the homotopy quotient of a $G$ action on $B(mathbb{Z}, G)$.
قيم البحث
اقرأ أيضاً
We calculate the ku-homology of the groups Z/p^n X Z/p and Z/p^2 X Z/p^2. We prove that for this kind of groups the ku-homology contains all the complex bordism information. We construct a set of generators of the annihilator of the ku-toral class. T
hese elements also generates the annihilator of the BP-toral class.
We calculate the annihilator of the ku-toral class for the p-groups Z_{p^2} X Z_{p^k}$ with k > 2. This allows us to give a description of the ku-homology of these groups.
We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show how these
theories can be obtained by looking at the action of a single isotropy group on a fiber of the anchor map, extending equivariant results for compact group actions. We also show how this extension from a single isotropy group to the entire groupoid action can be applied to the structure of principal bundles and classifying spaces.
We give an example of a compact connected Lie group of the lowest rank such that the mod 2 cohomology ring of its classifying space has a nonzero nilpotent element.
This paper studies the homology and cohomology of the Temperley-Lieb algebra TL_n(a), interpreted as appropriate Tor and Ext groups. Our main result applies under the common assumption that a=v+v^{-1} for some unit v in the ground ring, and states th
at the homology and cohomology vanish up to and including degree (n-2). To achieve this we simultaneously prove homological stability and compute the stable homology. We show that our vanishing range is sharp when n is even. Our methods are inspired by the tools and techniques of homological stability for families of groups. We construct and exploit a chain complex of planar injective words that is analogous to the complex of injective words used to prove stability for the symmetric groups. However, in this algebraic setting we encounter a novel difficulty: TL_n(a) is not flat over TL_m(a) for m<n, so that Shapiros lemma is unavailable. We resolve this difficulty by constructing what we call inductive resolutions of the relevant modules. Vanishing results for the homology and cohomology of Temperley-Lieb algebras can also be obtained from existence of the Jones-Wenzl projector. Our own vanishing results are in general far stronger than these, but in a restricted case we are able to obtain additional vanishing results via existence of the Jones-Wenzl projector. We believe that these results, together with the second authors work on Iwahori-Hecke algebras, are the first time the techniques of homological stability have been applied to algebras that are not group algebras.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
