Hopf algebras and invariants of the Johnson cokernel

Conant, Jim¹ ; Kassabov, Martin²

¹Department of Mathematics, University of Tennessee, Knoxville, TN 37996, United States
²Department of Mathematics, Cornell University, Ithaca, NY 14853, United States

Algebraic and Geometric Topology, Tome 16 (2016) no. 4, pp. 2325-2363

Résumé

We show that if H is a cocommutative Hopf algebra, then there is a natural action of Aut(Fn) on H⊗n which induces an Out(Fn) action on a quotient H⊗n¯. In the case when H = T(V ) is the tensor algebra, we show that the invariant TrC of the cokernel of the Johnson homomorphism studied in Algebr. Geom. Topol. 15 (2015) 801–821 projects to take values in Hvcd(Out(Fn);H⊗n¯). We analyze the n = 2 case, getting large families of obstructions generalizing the abelianization obstructions of Geom. Dedicata 176 (2015) 345–374.

Détail

DOI : 10.2140/agt.2016.16.2325

Classification : 20F65, 20J06, 16T05, 17B40, 20C15, 20F28
Keywords: Johnson homomorphism, Hopf algebras, automorphism groups of free groups

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