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arxiv: 2311.03121 · v2 · submitted 2023-11-06 · 🧮 math.AT

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The derived category of a locally compact space is rarely smooth

Oscar Harr
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classification 🧮 math.AT
keywords categorycompactderivedlocallysmoothspacediscretefinite
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We show that the derived category of a locally compact Hausdorff space $X$ is smooth in the sense of non-commutative geometry if and only if $X$ is discrete and finite.

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  1. Whitehead torsion and the kernel of assembly

    math.AT 2026-04 unverdicted novelty 6.0

    For spaces homeomorphic to finite simplicial complexes, the assembly functor admits a fully faithful right adjoint, yielding a Whitehead category and torsion cosheaf that recover Whitehead torsion via K-theory.