Explicit chain homotopy for the Alexander-Whitney, Eilenberg-Zilber pair
Clash Royale CLAN TAG#URR8PPP
$begingroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_A,Bcolon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_A,Bcolon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_A,Bcirc AW_A,Bsim Id_N_ast(Aotimes B).$$
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 Feb 23 at 23:24
David Roberts
17.5k463177
asked Feb 23 at 22:52
User371User371
1806
$endgroup$
add a comment |
$begingroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_A,Bcolon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_A,Bcolon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_A,Bcirc AW_A,Bsim Id_N_ast(Aotimes B).$$
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 Feb 23 at 23:24
David Roberts
17.5k463177
asked Feb 23 at 22:52
User371User371
1806
$endgroup$
add a comment |
$begingroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_A,Bcolon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_A,Bcolon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_A,Bcirc AW_A,Bsim Id_N_ast(Aotimes B).$$
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 Feb 23 at 23:24
David Roberts
17.5k463177
asked Feb 23 at 22:52
User371User371
1806
$endgroup$
Let $A$ and $B$ be simplicial abelian groups, and let $N_ast(-)$ denote the normalized chain complex functor. Let
$$AW_A,Bcolon N_ast(Aotimes B)
longrightarrow N_ast(A)otimes N_ast(B)$$
and
$$ EZ_A,Bcolon N_ast(A)otimes N_ast(B)
longrightarrow N_ast(Aotimes B)$$
denote the Alexander-Whitney map
and the Eilenberg-Zilber map respectively.
Does anyone know of an explicit chain homotopy realizing
$$EZ_A,Bcirc AW_A,Bsim Id_N_ast(Aotimes B).$$
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 Feb 23 at 23:24
David Roberts
17.5k463177
asked Feb 23 at 22:52
User371User371
1806
edited Feb 23 at 23:24
David Roberts
17.5k463177
asked Feb 23 at 22:52
User371User371
1806
edited Feb 23 at 23:24
David Roberts
17.5k463177
edited Feb 23 at 23:24
David Roberts
17.5k463177
edited Feb 23 at 23:24
David Roberts
17.5k463177
17.5k463177
asked Feb 23 at 22:52
User371User371
1806
asked Feb 23 at 22:52
User371User371
1806
asked Feb 23 at 22:52
User371User371
1806
1806
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
You have it in page 7 of this paper.
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
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active
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$begingroup$
You have it in page 7 of this paper.
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
$endgroup$
add a comment |
$begingroup$
You have it in page 7 of this paper.
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
$endgroup$
add a comment |
$begingroup$
You have it in page 7 of this paper.
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
$endgroup$
You have it in page 7 of this paper.
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
answered Feb 23 at 23:53
Fernando MuroFernando Muro
11.9k23465
11.9k23465
add a comment |
add a comment |
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