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arXiv 1306.6896math.AT
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面向组态空间的扫描

Scanning for oriented configuration spaces

Jeremy Miller, Martin Palmer

备注：
v2: 32 pages. Version 1 has been split into two parts. This is the second part (corresponding to section 3 in v1), substantially revised and incorporating the referee's corrections and suggestions; to appear in Homology, Homotopy and Applications. The first part (corresponding to section 2 of v1) has been separated into the preprint arXiv:1409.4389
发表信息：
Homology, Homotopy and Applications vol. 17 no. 1 (2015) pp. 35-66
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摘要：

在[Pal 13]（arXiv：1106.4540）中，第二作者证明了开连通流形上的“定向”构形空间序列在粒子数趋于无穷大时表现出同调稳定性。为了补充这一结果，我们确定相应的限制空间，直到同调等价，作为一个特定的明确的双覆盖的一个部分空间。同时证明了[McD75]中McDuff的扫描映射在无序构形空间上是极限非循环的。

英文摘要：

In [Pal13] (arXiv:1106.4540) the second author proved that the sequence of "oriented" configuration spaces on an open connected manifold exhibits homological stability as the number of particles goes to infinity. To complement that result we identify the corresponding limiting space, up to homology equivalence, as a certain explicit double cover of a section space. Along the way we also prove that the scanning map of McDuff in [McD75] for unordered configuration spaces is acyclic in the limit.

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