The de Rham homotopy theory and differential graded category
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- 作者：Syunji Moriya (1) moriyasy@math.kyoto-u.ac.jp
- 关键词：Rational homotopy theory – Non ; simply connected space – Dg ; category – Schematic homotopy type
- 刊名：Mathematische Zeitschrift
- 出版年：2012
- 出版时间：August 2012
- 年：2012
- 卷：271
- 期：3-4
- 页码：961-1010
- 全文大小：622.9 KB
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- ISSN：1432-1823
文摘
This paper is a generalization of Moriya (in J Pure Appl Algebra 214(4): 422–439, 2010). We develop the de Rham homotopy theory of not necessarily nilpotent spaces. We use two algebraic objects: closed dg-categories and equivariant dg-algebras. We see these two objects correspond in a certain way (Proposition 3.3.4, Theorem 3.4.5). We prove an equivalence between the homotopy category of schematic homotopy types (To?n in Selecta Math (N.S.), 12(1):39–135, 2006) and a homotopy category of closed dg-categories (Theorem 1.0.1). We give a description of homotopy invariants of spaces in terms of minimal models (Theorem 1.0.2). 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 (Bousfield and Kan in Lecture Notes in Mathematics, vol 304. Springer, Berlin, 1972) and closed dg-categories with subsidiary data (Theorem 1.0.4).