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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**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.

A symposium in honor of M. Morse). Princeton, 245–254 (1965) [44] E. Steinitz, Beitr¨ age zur Analysis situs. -Ber. Berl. Math. Ges. 7, 29–49 (1908) [45] D. P. Sullivan, Triangulating and smoothing homotopy equivalences and homeomorphisms. Geometric Topology Seminar Notes. Princeton (1967) (Published in this volume) [46] −, On the Hauptvermutung for manifolds. Bull. Amer. Math. Soc. 73, 598–600 (1967) [47] −, Geometric periodicity and the invariants of manifolds. Proc. 1970 Amsterdam Conference on Manifolds, Springer Lecture Notes in Mathematics 197, 44–75 (1971) ¨ [48] H.

P. Novikov, On manifolds with free abelian fundamental group and applications (Pontrjagin classes, smoothings, high-dimensional knots). Izv. Akad. Nauk SSSR, ser. mat. 30, 208–246 (1966) [32] Ch. Papakyriakopoulos, A new proof of the invariance of the homology groups of a complex. Bull. Soc. Math. Gr`ece 22, 1–154 (1943) [33] A. A. Ranicki, Algebraic L-theory and topological manifolds. Tracts in Mathematics 102, Cambridge (1992) [34] C. P. Rourke and B. J. Sanderson, On topological neighbourhoods.

### The Hauptvermutung Book by Ranicki A.A. (ed.)

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