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VOL. 52 | 2008 Symplectic automorphism groups of nilpotent quotients of fundamental groups of surfaces
Shigeyuki Morita

Editor(s) Robert Penner, Dieter Kotschick, Takashi Tsuboi, Nariya Kawazumi, Teruaki Kitano, Yoshihiko Mitsumatsu

Abstract

We describe the group version of the trace maps given in [29]. This gives rise to abelian quotients of symplectic IA-automorphism groups of nilpotent quotients of the fundamental groups of compact surfaces. By making use of them, we construct a representation of the group $\mathcal{H}_{g,1}$ of homology cobordism classes of homology cylinders introduced by Garoufalidis and Levine [6]. We define various cohomology classes of $\mathcal{H}_{g,1}$ and propose a few problems concerning them. In particular, we mention a possible relation to additive invariants for the group $\Theta_{\mathbb{Z}}^{3}$ of homology cobordism classes of homology 3-spheres.

Information

Published: 1 January 2008
First available in Project Euclid: 28 November 2018

zbMATH: 1166.57012
MathSciNet: MR2509720

Digital Object Identifier: 10.2969/aspm/05210443