String Topology, Euler Class and TNCZ free loop fibrations

2013/08/30 by Luc Menichi, Menichi, Luc · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1308.6684

openalex publication_date 2013/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a connected, closed oriented manifold. Let ω∈ H^m(M) be its orientation class. Let χ(M) be its Euler characteristic. Consider the free loop fibration ΩM\buildreli\over\hookrightarrow LM\buildrelev\over\twoheadrightarrow 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;\mathbbF_p)\twoheadrightarrow H^*(ΩM;\mathbbF_p) is onto then χ(M) is divisible by p (or M is a point).

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