Algebraic topology and formal group law

在Heisei 13中，我们主要研究了H. Miller给出的酉群的稳定分裂，并考虑了它的细化。酉群的同调是外代数。米勒分裂对应于外部代数的度分裂。另一方面。另一方面，利用Adams运算给出了在一个素数p处的局部分裂。我们已经证明，我们可以混合这些分裂，得到更细的分裂。在Heisei 14中，我们研究了mitchell - priddy光谱及其上同调。我们找到了一个生成器的最小集合作为Steenrod代数上的模。在平成15年，我们做了两个不同的研究。一是从一个新的角度研究Steenrod代数的结构。Steenrod代数的Hopf代数结构由Milnor确定，称为加性群律的自同构群。人们还不知道对这一事实的概念说明。我们通过结合乘法运算和Dickson不变量的概念给出了它。另一个研究是高维范畴的同伦理论。将离散范畴与dim 1中具有非平凡同伦群的空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