Rational homotopy theory and differential graded category

Details Rational homotopy theory and differential graded category Rational homotopy theory and differential graded category

2008-10-05

arxiv.org/abs/0810.0808v2

Mathematics

Algebraic Topology

28pages, revised version, title changed, to appear in JPAA

Scientific paper

We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the closed tensor dg-category of flat bundles on it much the same as the real homotopy type of a simply connected manifold is the de Rham algebra in original Sullivan's theory. We prove the existence of a model category structure on the category of small closed tensor dg-categories and as a most simple case, confirm an equivalence between the homotopy category of spaces whose fundamental groups are finite and whose higher homotopy groups are finite dimensional rational vector spaces and the homotopy category of small closed tensor dg-categories satisfying certain conditions.

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