论文标题
旋转映射课程组和二次符号组的同源稳定性
Homological stability of spin mapping class groups and quadratic symplectic groups
论文作者
论文摘要
我们使用细胞$ e_2 $ - 代数研究了表面旋转映射类和二次符号组的同源稳定性。我们会在其稳定性结果中得到改进，对于旋转映射班级组，我们表明是最佳的$ 2 $。我们还证明，在这两种情况下，$ \ mathbb {f} _2 $ - 本体学都满足次级同源稳定性。最后，我们全面描述了自旋映射类组的第一个同源组和二次符号组。
We study the homological stability of spin mapping class groups of surfaces and of quadratic symplectic groups using cellular $E_2$-algebras. We get improvements in their stability results, which for the spin mapping class groups we show to be optimal away from the prime $2$. We also prove that in both cases the $\mathbb{F}_2$-homology satisfies secondary homological stability. Finally, we give full descriptions of the first homology groups of the spin mapping class groups and of the quadratic symplectic groups.
