The Strong Novikov conjecture for finitely presented groups
Let be a finitely presented group, and let be its Rips complex for . Write for the equivariant localization algebra and for the reduced group -algebra. The evaluation map is
Strong Novikov conjecture. The induced map
is injective. This is the group-theoretic counterpart of the coarse Novikov conjecture, expressing injectivity of the assembly map for finitely presented groups. The source does not state whether it is resolved.
References
Primary source
Jinmin Wang and Bo Zhu, “Sharp bottom spectrum and scalar curvature rigidity”, arXiv:2408.08245 (2026).
Additional references
4 papers in this index state this conjecture (2007–2024). The statement above is taken from the most recent of them; the others are arXiv:1604.00464, arXiv:1603.01829, arXiv:0705.2578.
Progress summary
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