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2017 Cosimplicial groups and spaces of homomorphisms
Bernardo Villarreal
Algebr. Geom. Topol. 17(6): 3519-3545 (2017). DOI: 10.2140/agt.2017.17.3519

Abstract

Let G be a real linear algebraic group and L a finitely generated cosimplicial group. We prove that the space of homomorphisms Hom(Ln,G) has a homotopy stable decomposition for each n1. When G is a compact Lie group, we show that the decomposition is G–equivariant with respect to the induced action of conjugation by elements of G. In particular, under these hypotheses on G, we obtain stable decompositions for Hom(FnΓnq,G) and Rep(FnΓnq,G), respectively, where FnΓnq are the finitely generated free nilpotent groups of nilpotency class q1.

The spaces Hom(Ln,G) assemble into a simplicial space Hom(L,G). When G=U we show that its geometric realization B(L,U), has a nonunital E–ring space structure whenever Hom(L0,U(m)) is path connected for all m1.

Citation

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Bernardo Villarreal. "Cosimplicial groups and spaces of homomorphisms." Algebr. Geom. Topol. 17 (6) 3519 - 3545, 2017. https://doi.org/10.2140/agt.2017.17.3519

Information

Received: 11 July 2016; Revised: 26 March 2017; Accepted: 30 April 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1383.55003
MathSciNet: MR3709654
Digital Object Identifier: 10.2140/agt.2017.17.3519

Subjects:
Primary: 22E15
Secondary: 20G05, 55U10

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 6 • 2017
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