论文标题
幻影地图和纤维
Phantom maps and fibrations
论文作者
论文摘要
给定的指向$ cw $ - complexes $ x $和$ y $，$ \ rmph（x，y）$表示幻影映射的一组同型Phantom Maps类，从$ x $到$ y $和$ y $和$ \ rmsph（x，y）$表示$ \ \ rmph（x，y）$的子集（x，y）$由特殊phantom class of Phantom MAPS MAPS MAPS MAPS组成。在上一篇论文中，我们提供了足够的条件，以至于$ \ rmph（x，y）$和$ \ rmsph（x，y）$具有天然组结构，并建立了一个用于计算$ \ rmph（x，y）$和$ \ rmsph（x，x，y）$的公式，在许多情况下，在$中，$ [x，x，x，y. x，y.在本文中，我们建立了公式的双重版本，其中目标是振动的总空间，以计算对$ \ rmph（x，y）$和$ \ rmsph（x，y）的$（x，y）$（x，y）$（x，y）$的$（x，y）$，该公式或现有方法不适用。特别是，我们计算这些$ \ rmph（x，y）$和$ \ rmsph（x，y）$ $（x，y）$（x，y）$，使得$ x $是紧凑型lie $ g $的分类$ bg $ bg $ g $，$ y $ y $ y $ y是高度连接的cove $ y'\ langle n \ rangle n \ range $ y $ y n gbb y y gbb y' $ \ gbb = u，o $的h $由紧凑的谎言组$ h $。
Given pointed $CW$-complexes $X$ and $Y$, $\rmph(X, Y)$ denotes the set of homotopy classes of phantom maps from $X$ to $Y$ and $\rmsph(X, Y)$ denotes the subset of $\rmph(X, Y)$ consisting of homotopy classes of special phantom maps. In a preceding paper, we gave a sufficient condition such that $\rmph(X, Y)$ and $\rmsph(X, Y)$ have natural group structures and established a formula for calculating the groups $\rmph(X, Y)$ and $\rmsph(X, Y)$ in many cases where the groups $[X,Ω\widehat{Y}]$ are nontrivial. In this paper, we establish a dual version of the formula, in which the target is the total space of a fibration, to calculate the groups $\rmph(X, Y)$ and $\rmsph(X, Y)$ for pairs $(X,Y)$ to which the formula or existing methods do not apply. In particular, we calculate the groups $\rmph(X,Y)$ and $\rmsph(X,Y)$ for pairs $(X,Y)$ such that $X$ is the classifying space $BG$ of a compact Lie group $G$ and $Y$ is a highly connected cover $Y' \langle n \rangle$ of a nilpotent finite complex $Y'$ or the quotient $\gbb / H$ of $\gbb = U, O$ by a compact Lie group $H$.
