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On the wheeled PROP of stable cohomology of $\mathrm{Aut}(F_{n})$ with bivariant coefficients

Nariya Kawazumi and Christine Vespa

Algebraic & Geometric Topology 23 (2023) 3089–3128
Abstract

We show that the stable cohomology of automorphism groups of free groups with coefficients obtained by applying Hom (,) to tensor powers of the abelianization, is equipped with the structure of a wheeled PROP . We define another wheeled PROP by Ext –groups in the category of functors from the category of finitely generated free groups to k–modules. The main result of this paper is the construction of a morphism of wheeled PROPs φ: such that φ() is the wheeled PROP generated by the cohomology class h1 constructed by the first author.

Keywords
wheeled prop, cohomology of automorphisms of free groups
Mathematical Subject Classification
Primary: 20F28
Secondary: 18M85, 20J06
References
Publication
Received: 4 June 2021
Revised: 18 April 2022
Accepted: 3 May 2022
Published: 26 September 2023
Authors
Nariya Kawazumi
Department of Mathematical Sciences
University of Tokyo
Tokyo
Japan
Christine Vespa
Institut de Recherche Mathématique Avancée
Université de Strasbourg
Strasbourg
France

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