Explicit chain homotopy for the Alexander-Whitney, Eilenberg-Zilber pair
$begingroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_{A,B}colon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_{A,B}colon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_{A,B}circ AW_{A,B}sim Id_{N_ast(Aotimes B)}.$$
Motivation for its existence can be found in the comments of this question.
reference-request at.algebraic-topology homological-algebra simplicial-stuff abelian-categories
edited 3 hours ago
David Roberts
17.2k462176
asked 4 hours ago
User371User371
1686
$endgroup$
add a comment |
$begingroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_{A,B}colon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_{A,B}colon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_{A,B}circ AW_{A,B}sim Id_{N_ast(Aotimes B)}.$$
Motivation for its existence can be found in the comments of this question.
reference-request at.algebraic-topology homological-algebra simplicial-stuff abelian-categories
edited 3 hours ago
David Roberts
17.2k462176
asked 4 hours ago
User371User371
1686
$endgroup$
add a comment |
$begingroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_{A,B}colon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_{A,B}colon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_{A,B}circ AW_{A,B}sim Id_{N_ast(Aotimes B)}.$$
Motivation for its existence can be found in the comments of this question.
reference-request at.algebraic-topology homological-algebra simplicial-stuff abelian-categories
edited 3 hours ago
David Roberts
17.2k462176
asked 4 hours ago
User371User371
1686
$endgroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_{A,B}colon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_{A,B}colon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_{A,B}circ AW_{A,B}sim Id_{N_ast(Aotimes B)}.$$
Motivation for its existence can be found in the comments of this question.
reference-request at.algebraic-topology homological-algebra simplicial-stuff abelian-categories
reference-request at.algebraic-topology homological-algebra simplicial-stuff abelian-categories
edited 3 hours ago
David Roberts
17.2k462176
asked 4 hours ago
User371User371
1686
edited 3 hours ago
David Roberts
17.2k462176
asked 4 hours ago
User371User371
1686
edited 3 hours ago
David Roberts
17.2k462176
edited 3 hours ago
David Roberts
17.2k462176
edited 3 hours ago
David Roberts
17.2k462176
17.2k462176
asked 4 hours ago
User371User371
1686
asked 4 hours ago
User371User371
1686
asked 4 hours ago
User371User371
1686
1686
add a comment |
add a comment |
1 Answer
1
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$begingroup$
You have it in page 7 of this paper.
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
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active
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active
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$begingroup$
You have it in page 7 of this paper.
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
$endgroup$
add a comment |
$begingroup$
You have it in page 7 of this paper.
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
$endgroup$
add a comment |
$begingroup$
You have it in page 7 of this paper.
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
$endgroup$
You have it in page 7 of this paper.
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
answered 3 hours ago
Fernando MuroFernando Muro
11.6k23363
11.6k23363
add a comment |
add a comment |
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