A uniformly discrete bounded-geometry coarse disjoint union of finite connected uniformly bounded-degree graphs has an infinite-order class in degree-one coarse K-homology that maps to zero under maximal coarse assembly, so that map is not rationally injective.
A uniformly discrete bounded-geometry coarse disjoint union of finite connected uniformly bounded-degree graphs has an infinite-order class in degree-one coarse K-homology that maps to zero under maximal coarse assembly, so that map is not rationally injective.
A uniformly discrete bounded-geometry coarse disjoint union of finite connected uniformly bounded-degree graphs has an infinite-order class in degree-one coarse K-homology that maps to zero under maximal coarse assembly, so that map is not rationally injective.
If correct, extends the graph-union counterexample to the universal maximal Roe-algebra target.
Can maximal coarse assembly fail rational injectivity for bounded-geometry graph unions?
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OpenAI reports failure of maximal coarse assembly injectivity
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