论文标题
Mod 2 steenrod代数中ADEM关系的Cochain水平证明
A Cochain Level Proof of Adem Relations in the Mod 2 Steenrod Algebra
论文作者
论文摘要
1947年，新泽西州Steenrod使用明确的Cochain公式为Cocycles的Cup-I产品定义了Mod 2的同胞操作。后来，他使用群体同源性和无环模型方法而不是明确的Cochain公式以更一般的同源术语重塑了构建，以定义所有素数p的mod p操作。 Steenrod的学生J. Adem应用同源的观点，以证明由Steenrod行动产生的同学操作代数中证明了被称为ADEM关系的基本关系。在本文中，我们给出了Cochain级别的Mod 2 ADEM关系的证明。具体而言，给定一个Mod 2 Cocycle，我们使用Steenrod对方形操作的原始Cochain定义定义了施加在Cocycle上的Steenrod Asquares组成之间的ADEM关系。
In 1947, N.E. Steenrod defined the Steenrod Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup-i products of cocycles. He later recast the construction in more general homological terms, using group homology and acyclic model methods, rather than explicit cochain formulae, to define mod p operations for all primes p. Steenrod's student J. Adem applied the homological point of view to prove fundamental relations, known as the Adem relations, in the algebra of cohomology operations generated by the Steenrod operations. In this paper we give a proof of the mod 2 Adem relations at the cochain level. Specifically, given a mod 2 cocycle, we produce explicit cochain formulae whose coboundaries are the Adem relations among compositions of Steenrod Squares applied to the cocycle, using Steenrod's original cochain definition of the Square operations.
