论文标题
Riemann表面模量空间不稳定同源性的计算
Computations in the unstable homology of moduli spaces of Riemann surfaces
论文作者
论文摘要
在本文中，我们对模量空间的同源计算进行了调查，$ \ mathfrak {m} _ {g，1}^m $ riemann表面带有$ g \ geqslant 0 $，一条边界曲线和$ m \ geqslant 0 $ pumctures。尽管这个问题在理性和稳定上都有令人满意的答案，但不稳定的同源性仍然很复杂。我们讨论具有积分，MOD-2和合理系数的计算。此外，在大多数情况下，我们使用同源性操作确定明确的发电机。
In this article we give a survey of homology computations for moduli spaces $\mathfrak{M}_{g,1}^m$ of Riemann surfaces with genus $g\geqslant 0$, one boundary curve, and $m\geqslant 0$ punctures. While rationally and stably this question has a satisfying answer by the Madsen-Weiss theorem, the unstable homology remains notoriously complicated. We discuss calculations with integral, mod-2, and rational coefficients. Furthermore, we determine, in most cases, explicit generators using homology operations.
