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Higher operations in string topology of classifying spaces

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Abstract

Examples of non-trivial higher string topology operations have been regrettably rare in the literature. In this paper, working in the context of string topology of classifying spaces, we provide explicit calculations of a wealth of non-trivial higher string topology operations associated to a number of different Lie groups. As an application of these calculations, we obtain an abundance of interesting homology classes in the twisted homology groups of automorphism groups of free groups, the ordinary homology groups of holomorphs of free groups, and the ordinary homology groups of affine groups over the integers and the field of two elements.

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Acknowledgments

The author would like to thank Tilman Bauer, Gregory Ginot, Jesper Grodal, Richard Hepworth, Ib Madsen, Luc Menichi, Christine Vespa, Karen Vogtmann and Nathalie Wahl for useful conversations and the editor and the anonymous referee for valuable comments and suggestions.

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  1. Fachbereich Mathematik/AZ, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Anssi Lahtinen

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  1. Anssi Lahtinen
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Lahtinen, A. Higher operations in string topology of classifying spaces. Math. Ann. 368, 1–63 (2017). https://doi.org/10.1007/s00208-016-1406-1

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  • DOI: https://doi.org/10.1007/s00208-016-1406-1

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