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# Homology, Homotopy and Applications

## Volume 4 (2002)

### Number 2

### The Roos Festschrift volume

### An algebraic model for homotopy fibers

Pages: 117 – 139

DOI: https://dx.doi.org/10.4310/HHA.2002.v4.n2.a6

#### Authors

#### Abstract

Let $F$ be the homotopy fiber of a continuous map $f:X@>>>Y$, and let $R$ be a commutative, unitary ring. Given a morphism of chain Hopf algebras that models $(\Omega f)_{\sharp}:C_{*}(\Omega X;R)@>>>C_{*}(\Omega Y;R)$, we construct a cochain algebra that models $C^*(F;R)$. We explain how to simplify the model for certain large classes of maps $f$ and provide examples of the application of our model.

#### Keywords

homotopy fiber, algebraic model, Adams-Hilton model

#### 2010 Mathematics Subject Classification

55Pxx, 55T20, 55U15

Published 1 January 2002