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Results tagged with steenrod-algebra
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user 17787
7
votes
1
answer
939
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Associativity of Steenrod's cup-i product
In the paper Products of Cocycles and Extensions of Mappings,
Steenrod introduced the cup-i product (and Steenrod square). I would like to ask if Steenrod's cup-i product associative or not? The paper …
- 4,826
3
votes
1
answer
208
views
Cartan Formula for Steenrod square on cocycles
Let $x_n,y_n,\cdots$ be cocycles in $Z^n(X,\mathbb{Z}_2)$ (not cohomology classes in $H^n(X,\mathbb{Z}_2)$).
Let $Sq^k(x)\equiv x_n \cup_{n-k} x_n$ be the Steenrod square (This definition is valid for …
- 4,826
8
votes
2
answers
712
views
Adem relations of Steenrod square without modding out the coboundaries
In the paper Products of Cocycles and Extensions of Mappings,
Steenrod introduced the cup-$i$ product and Steenrod square $Sq^k$:
$$
Sq^k(x_n) \equiv x_n \smile_{n-k} x_n,\ \ \ x_n \in C^n(M^d;\math …
- 4,826