ترغب بنشر مسار تعليمي؟ اضغط هنا

Coformality around fibrations and cofibrations

54   0   0.0 ( 0 )
 نشر من قبل Ruizhi Huang
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Ruizhi Huang




اسأل ChatGPT حول البحث

We show that in a fibration the coformality of the base space implies the coformality of the total space under reasonable conditions, and these conditions can not be weakened. The result is partially dual to the classical work of Lupton cite{Lup} on the formality within a fibration. Our result has two applications. First, we show that for certain cofibrations, the coformality of the cofiber implies the coformality of the base. Secondly, we show that the total spaces of certain spherical fibrations are Koszul in the sense of Berglund cite{Ber}.



قيم البحث

اقرأ أيضاً

136 - Michael Harrison 2014
A fibration of ${mathbb R}^n$ by oriented copies of ${mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and Tabachnikov. A cl assification of smooth fibrations of ${mathbb R}^3$ by skew oriented lines was given by Salvai, in analogue with the classification of oriented great circle fibrations of $S^3$ by Gluck and Warner. We show that Salvais classification has a topological variation which generalizes to characterize all continuous fibrations of ${mathbb R}^n$ by skew oriented copies of ${mathbb R}^p$. We show that the space of fibrations of ${mathbb R}^3$ by skew oriented lines deformation retracts to the subspace of Hopf fibrations, and therefore has the homotopy type of a pair of disjoint copies of $S^2$. We discuss skew fibrations in the complex and quaternionic setting and give a necessary condition for the existence of a fibration of ${mathbb C}^n$ (${mathbb H}^n$) by skew oriented copies of ${mathbb C}^p$ (${mathbb H}^p$).
Given a path-connected space $X$ and $Hleqpi_1(X,x_0)$, there is essentially only one construction of a map $p_H:(widetilde{X}_H,widetilde{x}_0)rightarrow(X,x_0)$ with connected and locally path-connected domain that can possibly have the following t wo properties: $(p_{H})_{#}pi_1(widetilde{X}_H,widetilde{x}_0)=H$ and $p_H$ has the unique lifting property. $widetilde{X}_H$ consists of equivalence classes of paths starting at $x_0$, appropriately topologized, and $p_H$ is the endpoint projection. For $p_H$ to have these two properties, $T_1$ fibers are necessary and unique path lifting is sufficient. However, $p_H$ always admits the standard lifts of paths. We show that $p_H$ has unique path lifting if it has continuous (standard) monodromies toward a $T_1$ fiber over $x_0$. Assuming, in addition, that $H$ is locally quasinormal (e.g., if $H$ is normal) we show that $X$ is homotopically path Hausdorff relative to $H$. We show that $p_H$ is a fibration if $X$ is locally path connected, $H$ is locally quasinormal, and all (standard) monodromies are continuous.
We prove that the sectional category of the universal fibration with fibre X, for X any space that satisfies a well-known conjecture of Halperin, equals one after rationalization.
We show that the M-canonical map of an n-dimensional complex projective manifold X of Kodaira dimension two is birational to an Iitaka fibration for a computable positive integer M. M depends on the index b of a general fibre F of the Iitaka fibratio n and on the Betti number of the canonical covering of F, In particular, M is a universal constant if the dimension n is smaller than or equal to 4.
53 - Michael Lambert 2021
Presheaves on a small category are well-known to correspond via a category of elements construction to ordinary discrete fibrations over that same small category. Work of R. Pare proposes that presheaves on a small double category are certain lax fun ctors valued in the double category of sets with spans. This paper isolates the discrete fibration concept corresponding to this presheaf notion and shows that the category of elements construction introduced by Pare leads to an equivalence of virtual double categories.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا