The de Rham homotopy theory and differential graded category

Details The de Rham homotopy theory and differential graded category The de Rham homotopy theory and differential graded category

2009-12-24

arxiv.org/abs/0912.4844v2

Mathematics

Algebraic Topology

47 pages. final version. The final publication is available at http://www.springerlink.com

Scientific paper

10.1007/s00209-011-0899-2

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.

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