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2007 An algebraic model for the loop space homology of a homotopy fiber
Kathryn Hess, Ran Levi
Algebr. Geom. Topol. 7(4): 1699-1765 (2007). DOI: 10.2140/agt.2007.7.1699

Abstract

Let F denote the homotopy fiber of a map f:KL of 2–reduced simplicial sets. Using as input data the strongly homotopy coalgebra structure of the chain complexes of K and L, we construct a small, explicit chain algebra, the homology of which is isomorphic as a graded algebra to the homology of GF, the simplicial (Kan) loop group on F. To construct this model, we develop machinery for modeling the homotopy fiber of a morphism of chain Hopf algebras.

Essential to our construction is a generalization of the operadic description of the category DCSH of chain coalgebras and of strongly homotopy coalgebra maps given by Hess, Parent and Scott [Co-rings over operads characterize morphisms arxiv:math.AT/0505559] to strongly homotopy morphisms of comodules over Hopf algebras. This operadic description is expressed in terms of a general theory of monoidal structures in categories with morphism sets parametrized by co-rings, which we elaborate here.

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Kathryn Hess. Ran Levi. "An algebraic model for the loop space homology of a homotopy fiber." Algebr. Geom. Topol. 7 (4) 1699 - 1765, 2007. https://doi.org/10.2140/agt.2007.7.1699

Information

Received: 26 April 2007; Accepted: 2 October 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1182.55008
MathSciNet: MR2366176
Digital Object Identifier: 10.2140/agt.2007.7.1699

Subjects:
Primary: 16W30, 55P35
Secondary: 18D50, 18G55, 55U10, 57T05, 57T25

Rights: Copyright © 2007 Mathematical Sciences Publishers

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