ترغب بنشر مسار تعليمي؟ اضغط هنا

On the mod-$ell$ homology of the classifying space for commutativity

99   0   0.0 ( 0 )
 نشر من قبل Cihan Okay
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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

119 - Leticia Zarate 2010
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.
109 - Leticia Zarate 2010
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.
59 - Carla Farsi , Laura Scull , 2018
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.
341 - Masaki Kameko 2019
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.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا