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Marked fatgraph complexes and surface automorphisms

Kuno, Yusuke and Penner, R. C. and Turaev, Vladimir (2013) Marked fatgraph complexes and surface automorphisms. Geometriae Dedicata, 167 (1). pp. 151-166. ISSN 0046-5755.

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Combinatorial aspects of the Torelli–Johnson–Morita theory of surface automorphisms are extended to certain subgroups of the mapping class groups. These subgroups are defined relative to a specified homomorphism from the fundamental group of the surface onto an arbitrary group K. For K abelian, there is a combinatorial theory akin to the classical case, for example, providing an explicit cocycle representing the first Johnson homomophism with target Λ^3 K. Furthermore, the Earle class with coefficients in K is represented by an explicit cocyle.

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Additional Information:© 2012 Springer Science+Business Media Dordrecht. Received: 22 August 2012. Accepted: 18 November 2012. Published online: 28 November 2012. This work was done at the Center for Quantum Geometry of Moduli Spaces funded by the Danish National Research Foundation.
Funding AgencyGrant Number
Danish National Research FoundationUNSPECIFIED
Subject Keywords:Mapping class group; Torelli group; Fatgraph; Johnson homomorphism
Issue or Number:1
Classification Code:MSC 2000: 20F34; 32G15; 57N05
Record Number:CaltechAUTHORS:20131205-130456480
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Official Citation: Marked fatgraph complexes and surface automorphisms Yusuke Kuno, R. C. Penner, Vladimir Turaev Pages 151-166
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:42859
Deposited By: Ruth Sustaita
Deposited On:05 Dec 2013 21:19
Last Modified:03 Oct 2019 06:02

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