论文标题
链的简单结构链构成合理的同质类型，一次是素数。
The simplicial coalgebra of chains determines homotopy types rationally and one prime at a time
论文作者
论文摘要
我们证明，在连接的拓扑空间上，奇异链的简单性共同构造构成了同型类型的合理性，并且一次是质量的，而无需对基本组施加任何限制。特别是，在矢量空间的任意局部系统中具有系数的基本组和同源组完全取决于链的自然代数结构。代数结构以链条的简单性共同结构的类别表示，这是在函数从煤层造成的弱等价概念下，由亚当斯作为斗士建筑所产生的代数。基本组是由二次方程式确定的，该方程是关于归一化链的cobar构造的零同源性，该链涉及史坦罗德的链链同位素，以实现共同促成的共同互动性。具有局部系数的同源组是通过通用覆盖的代数类似物来建模的，该代数类似于我们对等效性弱的概念不变。我们猜想积分同拷贝类型还取决于整体链的简单界面，当通用覆盖物是有限类型时，我们证明了这一点。
We prove that the simplicial cocommutative coalgebra of singular chains on a connected topological space determines the homotopy type rationally and one prime at a time, without imposing any restriction on the fundamental group. In particular, the fundamental group and the homology groups with coefficients in arbitrary local systems of vector spaces are completely determined by the natural algebraic structure of the chains. The algebraic structure is presented as the class of the simplicial cocommutative coalgebra of chains under a notion of weak equivalence induced by a functor from coalgebras to algebras coined by Adams as the cobar construction. The fundamental group is determined by a quadratic equation on the zeroth homology of the cobar construction of the normalized chains which involves Steenrod's chain homotopies for cocommutativity of the coproduct. The homology groups with local coefficients are modeled by an algebraic analog of the universal cover which is invariant under our notion of weak equivalence. We conjecture that the integral homotopy type is also determined by the simplicial coalgebra of integral chains, which we prove when the universal cover is of finite type.
