Failure of rational injectivity for maximal coarse assembly. Constructs a uniformly discrete bounded-geometry space whose maximal coarse assembly map is not rationally injective. The example is a coarse disjoint union of finite connected graphs of uniformly bounded degree, with an infinite-order kernel class. A companion gives the analogous failure for reduced coarse assembly, disproving the rational coarse Novikov conjecture.
released 2026-10-05 | 1 theorem · 10 lemmas · 16 proofs · 9,859 words |
PLAY LEVEL 1 »(pdf)
We construct a uniformly discrete bounded-geometry space whose maximal coarse assembly map has an infinite-order element in its kernel. The space is a coarse disjoint union of finite connected graphs of uniformly bounded degree, so maximal coarse assembly need not be rationally injective even for such graph unions.
released 2026-09-23 | 1 theorem · 2 lemmas · 4 proofs · 6,495 words |
PLAY LEVEL 2 »(pdf)
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.