Free Cell Attachments and the Rational Homotopy Lie Algebra
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چکیده
Given a space X let LX denote its rational homotopy Lie algebra π∗(ΩX) ⊗ Q. A cell attachment f : ∨iSi → X is said to be free if the Lie ideal in LX generated by f is a free Lie algebra. This condition is shown to be general in the following sense. Given a space X with rational cone length N , then X is rationally homotopy equivalent to a space constructed using at most N + 1 free cell attachments. Algebraically, differential graded Lie algebras (dgLs) over Q are shown to be equivalent to separated dgLs. These results provide a method for calculating the rational homotopy Lie algebra and the homology of dgLs.
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تاریخ انتشار 2004