Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group

• Michael Borinsky ^[3] ; Benjamin Brück ^[1] ; Thomas Willwacher ^[2]
  1. [1] University of Münster

     University of Münster

     Kreisfreie Stadt Münster, Alemania

     
  2. [2] Swiss Federal Institute of Technology in Zurich

     Swiss Federal Institute of Technology in Zurich

     Zürich, Suiza

     
  3. [3] Institute for Theoretical Studies, ETH Zürich, Switzerland

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01018-9
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• Resumen

  • We compute the weight 2 cohomology of the Feynman transforms of the cyclic (co)operads BV and HyCom, and the top−2 weight cohomology of the Feynman transforms of DBV and Grav. Using a result of Giansiracusa, we compute, in particular, the top−2 weight cohomology of the handlebody group. We compare the result to the top−2 weight cohomology of the moduli space of curves Mg,n, recently computed by Payne and the last-named author. We also provide another proof of a recent result of Hainaut–Petersen identifying the top weight cohomology of the handlebody group with the Kontsevich graph cohomology.

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