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2016 Hopf algebras and invariants of the Johnson cokernel
Jim Conant, Martin Kassabov
Algebr. Geom. Topol. 16(4): 2325-2363 (2016). DOI: 10.2140/agt.2016.16.2325

Abstract

We show that if H is a cocommutative Hopf algebra, then there is a natural action of Aut(Fn) on Hn which induces an Out(Fn) action on a quotient Hn¯. 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);Hn¯). We analyze the n = 2 case, getting large families of obstructions generalizing the abelianization obstructions of Geom. Dedicata 176 (2015) 345–374.

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Jim Conant. Martin Kassabov. "Hopf algebras and invariants of the Johnson cokernel." Algebr. Geom. Topol. 16 (4) 2325 - 2363, 2016. https://doi.org/10.2140/agt.2016.16.2325

Information

Received: 17 September 2015; Revised: 20 January 2016; Accepted: 24 January 2016; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 06627577
MathSciNet: MR3546467
Digital Object Identifier: 10.2140/agt.2016.16.2325

Subjects:
Primary: 16T05, 17B40, 20F65, 20J06
Secondary: 20C15, 20F28

Rights: Copyright © 2016 Mathematical Sciences Publishers

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