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Homology manifolds and euclidean bundles

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arxiv 2406.14677 v2 pith:PSZE32OC submitted 2024-06-20 math.AT math.GT

classification math.ATmath.GT
keywords euclideanhomologyappearsbundlecomplexferryfibrationmanifold
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We construct a Poincar\'e complex whose periodic total surgery obstruction vanishes but whose Spivak normal fibration does not admit a reduction to a stable euclidean bundle. This contradicts the conjunction of two claims in the literature: Namely, on the one hand that a Poincar\'e complex with vanishing periodic total surgery obstruction is homotopy equivalent to a homology manifold, which appears in work of Bryant, Ferry, Mio and Weinberger, and on the other that the Spivak normal fibration of a homology manifold always admits a reduction to a stable euclidean bundle, which appears in work of Ferry and Pedersen.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Homology manifolds via six functor formalisms

    math.AT 2026-06 unverdicted novelty 7.0 of 10

    Using six functor formalisms, the authors prove that hypercomplete locally compact ANR homology manifolds are cohomologically smooth, that compact ANR homology manifolds are Poincaré duality complexes with Spivak tang...

  2. Survey on the Farrell-Jones Conjecture

    math.KT 2025-07 unverdicted

    The Farrell-Jones Conjecture is known for hyperbolic, CAT(0), arithmetic, and many other groups, and it implies a long list of conjectures about group rings and aspherical manifolds.

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