A Geometric Interpretation of Ranicki Duality

Abstract

Our main theorem provides an $(R,K)$ chain isomorphism: $T{\Delta }^{\ast }X\cong C(X_K)$. Here $T$ is the Ranicki Duality functor; ${\Delta }^{\ast }X$ is the simplicial cochain complex of the simplicial complex $X$, with control map $\pi :X\to K$ and $C(X_K)$ is the cellular chain complex of a CW complex $X_K$.

14 pages

References in corpus (1)

• Topological rigidity and actions on contractible manifolds with discrete singular set

Cited by in corpus (1)

• Chain duality for categories over complexes