Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 307-02. A counterexample to the coarse Novikov conjecture
Manuscript map · lines 8465–8474
OpenAI@2026-10-07#rem:oai-p-307-02
Authors: OpenAI. Family 307.
Title: A counterexample to the coarse Novikov conjecture.
Abstract: We disprove the coarse Novikov conjecture: ordinary coarse assembly need not be rationally injective for uniformly discrete spaces of bounded geometry. We construct a coarse disjoint union of finite graphs of uniformly bounded degree and an infinite-order class in its degree-one coarse K-homology whose image under ordinary coarse assembly in the K-theory of the reduced, locally compact Roe algebra vanishes.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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