اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA unifying view toward polyhedral products through panel structures
61
0
0.0
(
0
)
تأليف
Li Yu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A panel structure on a topological space is just a locally finite family of closed subspaces. A space together with a panel structure is called a space with faces. In this paper, we define the notion of polyhedral product over a space with faces. This notion provides a unifying viewpoint on the constructions of polyhedral products and generalized moment-angle complexes in various settings. We compute the stable decomposition of these spaces and use it to study their cohomology ring structures by the partial diagonal maps. Besides, we can compute the equivariant cohomology ring of the moment-angle complex over a space with faces with respect to the canonical torus action. The calculation leads to a notion of topological face ring of a space with faces, which generalizes the classical notion of face ring of a simplicial complex. We will see that many known results in the study of polyhedral products and moment-angle complexes can be reinterpreted from our general theorems on the polyhedral product over a space with faces. Moreover, we can derive some new results via our approach in some settings.
قيم البحث
اقرأ أيضاً
Polyhedral products were defined by Bahri, Bendersky, Cohen and Gitler, to be spaces obtained as unions of certain product spaces indexed by the simplices of an abstract simplicial complex. In this paper we give a very general homotopy theoretic cons
truction of polyhedral products over arbitrary pointed posets. We show that under certain restrictions on the poset $calp$, that include all known cases, the cohomology of the resulting spaces can be computed as an inverse limit over $calp$ of the cohomology of the building blocks. This motivates the definition of an analogous algebraic construction - the polyhedral tensor product. We show that for a large family of posets, the cohomology of the polyhedral product is given by the polyhedral tensor product. We then restrict attention to polyhedral posets, a family of posets that include face posets of simplicial complexes, and simplicial posets, as well as many others. We define the Stanley-Reisner ring of a polyhedral poset and show that, like in the classical cases, these rings occur as the cohomology of certain polyhedral products over the poset in question. For any pointed poset $calp$ we construct a simplicial poset $s(calp)$, and show that if $calp$ is a polyhedral poset then polyhedral products over $calp$ coincide up to homotopy with the corresponding polyhedral products over $s(calp)$.
A generalised Postnikov tower for a space $X$ is a tower of principal fibrations with fibres generalised Eilenberg-MacLane spaces, whose inverse limit is weakly homotopy equivalent to $X$. In this paper we give a characterisation of a polyhedral prod
uct $Z_K(X,A)$ whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower. We also include $p$-local and ration
The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitlers $J$-construction and simplicial wedge construction. This article gives a cohomological decomposition o
f a polyhedral product over a polyhedral join for certain families of pairs of simplicial complexes. A formula for the Hilbert-Poincar{e} series is given, which generalizes Ayzenbergs formula for the moment-angle complex.
We show that the tensor product of two cyclic $A_infty$-algebras is, in general, not a cyclic $A_infty$-algebra, but an $A_infty$-algebra with homotopy inner product. More precisely, we construct an explicit combinatorial diagonal on the pairahedra,
which are contractible polytopes controlling the combinatorial structure of an $A_infty$-algebra with homotopy inner products, and use it to define a categorically closed tensor product. A cyclic $A_infty$-algebra can be thought of as an $A_infty$-algebra with homotopy inner products whose higher inner products are trivial. However, the higher inner products on the tensor product of cyclic $A_infty$-algebras are not necessarily trivial.
We selected a sample of 33 Gamma Ray Bursts (GRBs) detected by Swift, with known redshift and optical extinction at the host frame. For these, we constructed the de-absorbed and K-corrected X-ray and optical rest frame light curves. These are modelle
d as the sum of two components: emission from the forward shock due to the interaction of a fireball with the circum-burst medium and an additional component, treated in a completely phenomenological way. The latter can be identified, among other possibilities, as late prompt emission produced by a long lived central engine with mechanisms similar to those responsible for the production of the standard early prompt radiation. Apart from flares or re-brightenings, that we do not model, we find a good agreement with the data, despite of their complexity and diversity. Although based in part on a phenomenological model with a relatively large number of free parameters, we believe that our findings are a first step towards the construction of a more physical scenario. Our approach allows us to interpret the behaviour of the optical and X-ray afterglows in a coherent way, by a relatively simple scenario. Within this context it is possible to explain why sometimes no jet break is observed; why, even if a jet break is observed, it is often chromatic; why the steepening after the jet break time is often shallower than predicted. Finally, the decay slope of the late prompt emission after the shallow phase is found to be remarkably similar to the time profile expected by the accretion rate of fall-back material (i.e. proportional to t^{-5/3}), suggesting that this can be the reason why the central engine can be active for a long time.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
