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Mar 6, 2014 at 23:52 comment added D.-C. Cisinski If you keep track of the algebra structure defined by the cup product of cochains in an adequate sense, you can detect the homotopy type of simply connected spaces (or even of nilpotent spaces), and you can also detect homotopy classes of continuous maps between these. See the paper of M. A. Mandell "Cochains and Homotopy Type", Publ. Math. IHES, 103 (2006), 213-246 (also available on arXiv).
Mar 6, 2014 at 17:43 answer added Leo Alonso timeline score: 7
Jul 4, 2013 at 7:25 review Close votes
Jul 5, 2013 at 0:51
May 26, 2010 at 16:56 answer added thel timeline score: 7
May 26, 2010 at 16:29 comment added Torsten Ekedahl The map $X \mapsto C_X$ does not induce an injection on isomorphism classes. In order to apply th Whitehead theorem you need a map first.
May 26, 2010 at 16:02 history asked Heinrich Hartmann CC BY-SA 2.5