String Topology, Euler Class and TNCZ free loop fibrations

الأصل · EN

Let M be a connected, closed oriented manifold. Let ω∈ Hᵐ(M) be its orientation class. Let χ(M) be its Euler characteristic. Consider the free loop fibration ΩMi LMev M. For any class a∈ H*(LM) of positive degree, we prove that the cup product χ(M)a∪ ev*(ω) is null. In particular, if i*:H*(LM;Fₚ) H*(ΩM;Fₚ) is onto then χ(M) is divisible by p (or M is a point).