HOMOTOPY LIE-ALGEBRAS AND FUNDAMENTAL-GROUPS VIA DEFORMATION-THEORY

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*OMEGAS (the homotopy Lie algebra) or gr*pi1S (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.