The simplicial coalgebra of chains determines homotopy types rationally and one prime at a time
The simplicial coalgebra of chains determines homotopy types rationally and one prime at a time
复制标题
链的单纯余代数有理地确定同伦类型并一次确定一个素数
DOI：
10.1090/tran/8579
复制
发表时间：
2022
影响因子：
1.3
通讯作者：
Zeinalian, Mahmoud
中科院分区：
文献类型：
--
作者：
Rivera, Manuel;Wierstra, Felix;Zeinalian, Mahmoud
证明了连通拓扑空间上奇异链的单纯余交换余代数在不对基本群施加任何限制的情况下，有理地确定同伦型，且每次确定一个素数.特别地，向量空间的任意局部系中的基本群和系数同调群完全由链的自然代数结构决定。代数结构被表示为链的单余交换余代数类，在弱等价的概念下，由从余代数到代数的函子诱导，亚当斯作为cobar构造提出。基本组是由一个二次方程的cobar建设的规范化链，其中涉及Steenrod的链同伦的余积的余交换性的第零个同源性。具有局部系数的同调群由在我们的弱等价概念下不变的泛覆盖的代数模拟来建模。我们猜想，积分同伦类型也是由积分链的单纯余代数，我们证明了当通用覆盖是有限型。引用
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. References
登录
查看更多内容
影响因子：
1.1
作者：
Urtzi Buijs;Yves F'elix;A. Murillo;Daniel Tanr'e
通讯作者：
Daniel Tanr'e
幺半群的同伦理论和派生局域化
DOI：
10.48550/arxiv.1810.00373
发表时间：
2018
期刊：
arXiv e-prints
影响因子：
--
作者：
Chuang Joe
通讯作者：
Chuang Joe
DOI：
10.1090/s0065-9266-2010-00631-8
发表时间：
2009-05
期刊：
arXiv: Category Theory
影响因子：
--
作者：
L. Positselski
通讯作者：
L. Positselski
纤维化的立方模型
影响因子：
0.8
作者：
T. Kadeishvili;S. Saneblidze
通讯作者：
S. Saneblidze
余代数的单纯预滑
影响因子：
0.7
作者：
G. Raptis
通讯作者：
G. Raptis