论文标题
通过共同体学代数的合理同副本类型的映射空间
Rational homotopy type of mapping spaces via cohomology algebras
论文作者
论文摘要
In this paper, we show that for finite $CW$-complexes $X$ and two-stage space $Y$ (for example $n$-spheres $S^n$, homogeneous spaces and $F_0$-spaces), the rational homotopy type of $\map(X, Y)$ is determined by the cohomology algebra $H^*(X; \Q)$ and the rational homotopy type of $ y $。从中，假设$ x $和$ y $的同构代数是同构的，我们将在映射空间$ \ map（x，y）$的组件上的成分上的存在。最后，如果相应的\ emph {maurer-cartan elements}通过$ h^\ ast（x，\ q）$连接，我们将证明$ \ map（x，y; f）\ simeq \ map（x，y; f'）$。
In this paper, we show that for finite $CW$-complexes $X$ and two-stage space $Y$ (for example $n$-spheres $S^n$, homogeneous spaces and $F_0$-spaces), the rational homotopy type of $\map(X, Y)$ is determined by the cohomology algebra $H^*(X; \Q)$ and the rational homotopy type of $Y$. From this, we deduce the existence of H-structures on a component of the mapping space $\map(X, Y)$, assuming the cohomology algebras of $X$ and $Y$ are isomorphism. Finally, we will show that $\map(X, Y; f)\simeq\map(X, Y; f')$ if the corresponding \emph{Maurer-Cartan elements} are connected by an algebra automorphism of $H^\ast(X, \Q)$.
