论文标题
全球Mackey函数的分裂和e夫欧拉类的规律性
Splittings of global Mackey functors and regularity of equivariant Euler classes
论文作者
论文摘要
我们为正交，统一和符号型组的全球Mackey函子的值建立了自然分裂。特别是，相邻维度的正交，统一和符号成群之间的限制统一是自然裂解的赋形剂。对分裂的兴趣来自于稳定同型理论。每个全局频谱的稳定同质组构成一个全局的Mackey函数，因此分裂意味着某些长的精确同型组序列分为短精确序列。对于真实而复杂的全局thom Spectra $ \ Mathbf {Mo} $和$ \ Mathbf {Mu} $，分割意味着与$ O（n）$和$ U（n）$的重言式表示相关的各种Euler类的规律性。
We establish natural splittings for the values of global Mackey functors at orthogonal, unitary and symplectic groups. In particular, the restriction homomorphisms between the orthogonal, unitary and symplectic groups of adjacent dimensions are naturally split epimorphisms. The interest in the splitting comes from equivariant stable homotopy theory. The equivariant stable homotopy groups of every global spectrum form a global Mackey functor, so the splittings imply that certain long exact homotopy group sequences separate into short exact sequences. For the real and complex global Thom spectra $\mathbf{MO}$ and $\mathbf{MU}$, the splittings imply the regularity of various Euler classes related to the tautological representations of $O(n)$ and $U(n)$.
