Homotopy Lie algebras and fundamental groups via deformation theory

Markl, Martin; Papadima, Stefan

Annales de l'Institut Fourier, Tome 42 (1992) no. 4, pp. 905-935.

Nous donnons les premiers résultats de notre plus vaste projet en fixant d’abord quelques invariants facilement accessibles des espaces topologiques (par exemple le cup-produit en basses dimensions) et en étudiant alors la variation d’invariants plus complexes tels que $\pi *\Omega S$ (l’algèbre de Lie homotopique) ou bien ${gr}^{*}{\pi }_{1}S$ (l’algèbre de Lie graduée associée aux séries centrales du groupe fondamental). Nous donnons des résultats fondamentaux de rigidité, ainsi qu’une application à la topologie en basses dimensions.

We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as ${\pi }_{*}\Omega S$ (the homotopy Lie algebra) or ${gr}^{*}{\pi }_{1}S$ (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.

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