Pontrjagin-Thom映射与稳定曲线模栈的同调
Pontrjagin-Thom maps and the homology of the moduli stack of stable curves
摘要：
研究亏格g上稳定n点复曲线模叠加的奇异同调（带场系数）（Deligne-Mumford紧化）.它的每一个不可约边界分量通过Pontrjagin-Thom构造确定一个到某个无限闭路空间的映射，该无限环路空间的同调是很好理解的。我们表明，这些地图是满射的同调在一定范围内的程度成比例的属。这意味着在模栈的同调中存在许多新的挠类。
英文摘要：
We study the singular homology (with field coefficients) of the moduli stack of stable n-pointed complex curves of genus g (the Deligne-Mumford compactification). Each of its irreducible boundary components determines via the Pontrjagin-Thom construction a map to a certain infinite loop space whose homology is well understood. We show that these maps are surjective on homology in a range of degrees proportional to the genus. This implies the existence of many new torsion classes in the homology of the moduli stack.
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