By Ranicki A.A. (ed.)

A set of papers at the topology of manifolds through A.A.Ranicki (editor), A.J.Casson, D.P.Sullivan, M.A.Armstrong, C.P.Rourke, and G.E.Cooke

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Additional resources for The Hauptvermutung Book

Example text

C. Whitehead [18], there is a based polyhedron GF /P LF and a homotopy equivalence i : GF /P LF −−→L. Define χ1 = χ i : GF /P LF −−→B P LF . Let B be a based cell complex and let F be a compact P L manifold. A GF /P LF -bundle over B consists of a block bundle ξ over B with fibre F and a P L map t : E(ξ), E(∂ξ) −−→ F, ∂F such that tb(ξ) = 1. Two GF /P LF -bundles (ξ, t) and (η, u) over B are isomorphic if there is an isomorphism h : ξ−−→η such that uh t (rel b(ξ)(F )). Define casson 48 the equivalence of GF /P LF -bundles over a polyhedron X as in Chapter I, and let JF (X) be the set of equivalence classes.

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