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

Malin, Connor

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.

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