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de Rham
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მამუკა ჯიბლაძე
მამუკა ჯიბლაძე
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Does the polynomial De RahmRham functor preserves finite cartesian products?

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De RahmRham functor on simplicial sets. I have the following questions

  1. When we have a quasi-isomorphism between $\Omega^{*}_{\text{poly}}\left(K\times L\right)$ and $\Omega^{*}_{\text{poly}}\left(K\right)\otimes \Omega^{*}_{\text{poly}}\left( L\right)$?

  2. When we have an ISOMORPHISM?(Conjecture: if $K$ or $L$ is a finite simplicial set)

Here $dg_{\geq 0}Comm_{+}$ is the category of commutative unitary cochain differential graded algebras over a field of char zero.

Thanks!!!

Does the polynomial De Rahm functor preserves finite cartesian products?

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets. I have the following questions

  1. When we have a quasi-isomorphism between $\Omega^{*}_{\text{poly}}\left(K\times L\right)$ and $\Omega^{*}_{\text{poly}}\left(K\right)\otimes \Omega^{*}_{\text{poly}}\left( L\right)$?

  2. When we have an ISOMORPHISM?(Conjecture: if $K$ or $L$ is a finite simplicial set)

Here $dg_{\geq 0}Comm_{+}$ is the category of commutative unitary cochain differential graded algebras over a field of char zero.

Thanks!!!

Does the polynomial De Rham functor preserves finite cartesian products?

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rham functor on simplicial sets. I have the following questions

  1. When we have a quasi-isomorphism between $\Omega^{*}_{\text{poly}}\left(K\times L\right)$ and $\Omega^{*}_{\text{poly}}\left(K\right)\otimes \Omega^{*}_{\text{poly}}\left( L\right)$?

  2. When we have an ISOMORPHISM?(Conjecture: if $K$ or $L$ is a finite simplicial set)

Here $dg_{\geq 0}Comm_{+}$ is the category of commutative unitary cochain differential graded algebras over a field of char zero.

Thanks!!!

deleted 2 characters in body; edited title
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Cepu
Cepu
  • 1.4k
  • 8
  • 13

Does the polynomial De Rahm functor preserves finite cartesian products?

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets. I have the following questions

  1. When we have a quasi-isomorphism between $\Omega^{*}_{\text{poly}}\left(K\times L\right)$ and $\Omega^{*}_{\text{poly}}\left(K\right)\otimes \Omega^{*}_{\text{poly}}\left( L\right)$?

  2. When we have an ISOMORPHISM?(Conjecture: whenif $K$ or $L$ is a finite simplicial set)

Here $dg_{\geq 0}Comm_{+}$ is the category of commutative unitary cochain differential graded algebras over a field of char zero.

Thanks!!!

Does the polynomial De Rahm functor preserves finite cartesian products

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets. I have the following questions

  1. When we have a quasi-isomorphism between $\Omega^{*}_{\text{poly}}\left(K\times L\right)$ and $\Omega^{*}_{\text{poly}}\left(K\right)\otimes \Omega^{*}_{\text{poly}}\left( L\right)$?

  2. When we have an ISOMORPHISM?(Conjecture: when $K$ or $L$ is a finite simplicial set)

Here $dg_{\geq 0}Comm_{+}$ is the category of commutative unitary cochain differential graded algebras over a field of char zero.

Thanks!!!

Does the polynomial De Rahm functor preserves finite cartesian products?

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets. I have the following questions

  1. When we have a quasi-isomorphism between $\Omega^{*}_{\text{poly}}\left(K\times L\right)$ and $\Omega^{*}_{\text{poly}}\left(K\right)\otimes \Omega^{*}_{\text{poly}}\left( L\right)$?

  2. When we have an ISOMORPHISM?(Conjecture: if $K$ or $L$ is a finite simplicial set)

Here $dg_{\geq 0}Comm_{+}$ is the category of commutative unitary cochain differential graded algebras over a field of char zero.

Thanks!!!

Source Link
Cepu
Cepu
  • 1.4k
  • 8
  • 13

Does the polynomial De Rahm functor preserves finite cartesian products

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets. I have the following questions

  1. When we have a quasi-isomorphism between $\Omega^{*}_{\text{poly}}\left(K\times L\right)$ and $\Omega^{*}_{\text{poly}}\left(K\right)\otimes \Omega^{*}_{\text{poly}}\left( L\right)$?

  2. When we have an ISOMORPHISM?(Conjecture: when $K$ or $L$ is a finite simplicial set)

Here $dg_{\geq 0}Comm_{+}$ is the category of commutative unitary cochain differential graded algebras over a field of char zero.

Thanks!!!