{"id":"openai-math/A-counterexample-to-the-coarse-Novikov-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026","tags":["coarse-geometry","k-theory","roe-algebras","coarse-assembly"],"score":0,"title":"A counterexample to the coarse Novikov conjecture","domain":"Topology","family":"307","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Failure of rational injectivity for maximal coarse assembly"}