2
$\begingroup$

To every simplicial manifold is associated its simplicial deRham complex.

Is there any literature that discusses explicitly to which extent this classical construction, regarded as a (contravariant) functor from simplicial manifolds to dg-algebras, is homotopical?

For instance: simplicial manifolds naturally embed into the category of simplicial presheaves on the category of manifolds, on which we have the standard local model structure on simplicial presheaves. On dg-algebras there is the standard model structure on dg-algebras.

Is there any literature that discusses explicitly the respect of the simplicial deRham complex operation of the respective weak equivalences?

Improve this question
$\endgroup$
4
  • $\begingroup$ Some of this is handled in the nLab, I believe, and there are some references dotted around in the relevant entries. $\endgroup$
    – Tim Porter
    Apr 13, 2011 at 6:13
  • $\begingroup$ This paper: front.math.ucdavis.edu/0810.1747 contains a covariant version of simplicial de Rham theory, with good categorical properties. I wrote it with applications to model structures in mind, although no such applications are actually in the paper. $\endgroup$
    – Neil Strickland
    Apr 13, 2011 at 6:43
  • $\begingroup$ Could someone retag this? (I'm not really competent to do it myself.) $\endgroup$
    – Yemon Choi
    Apr 13, 2011 at 7:53
  • $\begingroup$ I retagged it, but did not take flags off, maybe I should have. $\endgroup$
    – Sean Tilson
    Apr 13, 2011 at 12:14

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.