The Strong Novikov conjecture for finitely presented groups
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.
Sources & referencesView supporting material
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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