Algebraic topology and formal group law

在平成13中，我们主要研究了H.Miller给出的酉群的稳定分裂，并考虑了它的改进。酉群的同调是外代数。米勒分裂对应于外代数的度分裂。在另一端。另一方面，利用Adams运算给出了素数p处的局部分裂。我们已经证明，我们可以混合这些分裂，并得到翅片分裂。在平成14中，我们研究了Mittchell-Priddy谱及其上同调。我们找到了作为Steenrod代数上的模的极小生成元集合。在平成15，我们做了两个不同的研究。一是从新的角度研究Steenrod代数的结构。Steenrod代数的Hopf代数结构是由Milnor决定的，它与加法群律的自同构群相同。这一事实的概念性阐述尚不为人所知。我们通过结合乘法运算和Dickson不变量的概念给出了这一点。另一个研究是高维范畴的同伦理论。将离散范畴与维1中具有非平凡同伦群的空间之间的对应关系推广到2个范畴

In Heisei 13, we studied mainly the stable splitting, of Unitary groups given by H. Miller, and considerd its refinment. The homology of Unitary groups are the exterior algebras. Miller's splitting correspond to the degreewise splitting of the exterior algebra. On the other. hand, local splitting at a prime p was given by using the Adams operation. We have shown that we can mix these splittings and obtainned the finner splitting. In Heisei 14, we studied the Mittchell-Priddy spectrum and its cohomology. We found a minimal set of generators as the module over the Steenrod algebra. In Heisei 15, we made two different stdies. One is the study of the structure of Steenrod algebra from a new point of view. The Hopf algebra structure of the Steenrod algebra was determined by Milnor and known the same as the automorphism group of the additive group law. It was not known the conceptional exposition of this fact. We gave this by combining notions of multiplicative operations and the Dickson invariants. The other study is homotopy theory of higher dimensional category. Correspondence between discrete categories and spaces with non-trivial homotopy group in dim 1 is extended to 2 categories