论文标题
Cochain Level May-Steenrod操作
Cochain level May-Steenrod operations
论文作者
论文摘要
Steenrod在1947年定义了Mod 2的STEENROD广场，并使用杯子$ i $产品的显式科链公式在空间的空间上进行了。一个连贯的同型家族源自亚历山大的破碎对称性，亚历山大 - 惠特尼的链条近似对角。后来，他使用对称群体的同源性为所有素数定义了他的同义操作。这种方法增强了对操作的概念理解，并允许许多进步，但缺乏其定义的具体性。近年来，由于共同研究的新应用，需要有效地对Steenrod操作进行可计算的定义成为一个关键问题。利用5月的经营观点，本文在所有介绍的多种经营中提供了这样的定义，这些定义将steenrod杯 - $ i $产品推广到空间的简单和立方体方面。
Steenrod defined in 1947 the Steenrod squares on the mod 2 cohomology of spaces using explicit cochain formulae for the cup-$i$ products; a family of coherent homotopies derived from the broken symmetry of Alexander--Whitney's chain approximation to the diagonal. He later defined his homonymous operations for all primes using the homology of symmetric groups. This approach enhanced the conceptual understanding of the operations and allowed for many advances, but lacked the concreteness of their definition at the even prime. In recent years, thanks to the development of new applications of cohomology, the need to have an effectively computable definition of Steenrod operations has become a key issue. Using the operadic viewpoint of May, this article provides such definitions at all primes introducing multioperations that generalize the Steenrod cup-$i$ products on the simplicial and cubical cochains of spaces.
