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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