Constructions of cocycles of finite groups by characteristic classes

对于具有单群G的紧致Riemann曲面的有限伽罗瓦覆盖，我们利用群上同调中的转移同态和Kawazumi-Uemura公式构造了表示与伽罗瓦覆盖相关的特征类（mumford - morta - miller类）的环。此外，我们利用“周期性现象”和Steenrod操作构造了这类的模p环。此外，我们还证明了Coxeter群的p-局部同调的一个消失定理。其关键成分是cox复合物的等变同源性。

For a finite Galois covering of a compact Riemann surface with a monodromy group G, we constructed cocycles representing the characteristic classes (Mumford-Morita-Miller classes) associated with a Galois covering, by using transfer homomorphisms in group cohomology and Kawazumi-Uemura formula. In addition, we construct mod p cocycles for such classes by using "periodicity phenomena" and Steenrod operations. Moreover, we prove a vanishing theorem for p-local homology of Coxeter groups. The key ingredient was equivariant homology of Coxeter complexes.