论文标题
稳定配置空间的同质不变性的基本证明
An elementary proof of the homotopy invariance of stabilized configuration spaces
论文作者
论文摘要
在本文中，我们给出了基本证明，证明了拓扑歧管$ M $的配置空间的等效稳定同型类型$ f（m，k）$的适当同型不变性。我们的技术是计算$σ^\ infty_+ f（m，k）$的西紫红色双头双重双重双重二重奏，并在正常的球形纤维上使用Spivak和Wall的结果推断出Spanier-White-Whitehead Dual是合适的同质型。 Knudsen最近使用分解同源性证明了这种稳定的不变性。除了小学之外，我们的证据还具有一个优势，即它很容易扩展到最近进行了研究的``广义配置空间''。
In this paper we give an elementary proof of the proper homotopy invariance of the equivariant stable homotopy type of the configuration space $F(M,k)$ for a topological manifold $M$. Our technique is to compute the Spanier-Whitehead dual of $Σ^\infty_+ F(M,k)$ and use the results of Spivak and Wall on normal spherical fibrations to deduce that the Spanier-Whitehead dual is a proper homotopy invariant. This stable invariance was recently proved by Knudsen using factorization homology. Aside from being elementary, our proof has the advantage that it readily extends to ``generalized configuration spaces'' which have recently undergone study.
