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VOL. 72 | 2017 Homomorphisms on groups of volume-preserving diffeomorphisms via fundamental groups
Tomohiko Ishida

Editor(s) Taro Asuke, Shigenori Matsumoto, Yoshihiko Mitsumatsu

Abstract

Let $M$ be a closed manifold. Polterovich constructed a linear map from the vector space of quasi-morphisms on the fundamental group $\pi_{1}(M)$ of $M$ to the space of quasi-morphisms on the identity component $\mathrm{Diff}_{\Omega}^{\infty} (M)_{0}$ of the group of volume-preserving diffeomorphisms of $M$. In this paper, the restriction $H^{1}(\pi_{1}(M); \mathbb{R}) \to H^{1}(\mathrm{Diff}_{\Omega}^{\infty} (M)_{0}; \mathbb{R})$ of the linear map is studied and its relationship with the flux homomorphism is described.

Information

Published: 1 January 2017
First available in Project Euclid: 4 October 2018

zbMATH: 1388.37031
MathSciNet: MR3726720

Digital Object Identifier: 10.2969/aspm/07210387

Subjects:
Primary: 37C15

Rights: Copyright © 2017 Mathematical Society of Japan

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