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An algebraic model for homotopy fibers

Nicolas Dupont and Kathryn Hess

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 $(\Om f)\sb {\sharp}:C_{*}(\Om X;R)@>>>C_{*}(\Om Y;R)$, 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.

Homology, Homotopy and Applications, Vol. 4(2), 2002, pp. 117-139

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