Homomorphisms on groups of volume-preserving diffeomorphisms via fundamental groups

2014/08/12 by Tomohiko Ishida, Ishida, Tomohiko
Mathematics · #37C15 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1408.2669

openalex publication_date 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a closed manifold. Polterovich constructed a linear map from the vector space of quasi-morphisms on the fundamental group π₁(M) of M to the space of quasi-morphisms on the identity component \rm Diff_Ω^∞ (M)₀ of the group of volume-preserving diffeomorphisms of M. In this paper, the restriction H¹(π₁(M); \mathbb R)→ H¹(\rm Diff_Ω^∞ (M)₀ ; \mathbb R) of the linear map is studied and its relationship with the flux homomorphism is described.

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