un 9 4 Strongly homotopy Lie algebras Tom Lada

Strongly homotopy Lie algebras first made their appearance in a supporting role in deformation theory [11]. The philosophy that every deformation problem is directed by a differential graded Lie algebra leads, in the context of deformation theory of a differential graded algebra A, to a spectral sequence of which the E2-term is naturally a strongly homotopy Lie algebra. For a topological space S, the homotopy groups π∗(ΩS) form a graded Lie algebra which can be extended non-trivially (though non-canonically) to a strongly homotopy Lie algebra which reflects more accurately the homotopy type of S. The relevant operations represent the higher order Whitehead products on S. In the stable range, the basic products are given by composition and higher order composition products; more details are given in [12]).