The de Rham homotopy theory and differential graded category
Abstract
This paper is a generalization of arXiv:0810.0808. We develop the de Rham homotopy theory of not necessarily nilpotent spaces, using closed dg-categories and equivariant dg-algebras. We see these two algebraic objects correspond in a certain way. We prove an equivalence between the homotopy category of schematic homotopy types and a homotopy category of closed dg-categories. We give a description of homotopy invariants of spaces in terms of minimal models. The minimal model in this context behaves much like the Sullivan's minimal model. We also provide some examples. We prove an equivalence between fiberwise rationalizations and closed dg-categories with subsidiary data.
Keywords
Cite
@article{arxiv.0912.4844,
title = {The de Rham homotopy theory and differential graded category},
author = {Syunji Moriya},
journal= {arXiv preprint arXiv:0912.4844},
year = {2020}
}
Comments
47 pages. final version. The final publication is available at http://www.springerlink.com