Exotic spheres Σ^d (d ≢ 1 mod 4) are detected by the homotopy type of their truncated Disc-presheaf under conditions established via gluing, duality, and mapping class group computations.
Prigge, On tautological classes of fibre bundles and self-embedding calculus, PhD thesis, University of Cambridge (2020), https://www.repository.cam.ac.uk/handle/1810/317892
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Framed configuration spaces and exotic spheres
Exotic spheres Σ^d (d ≢ 1 mod 4) are detected by the homotopy type of their truncated Disc-presheaf under conditions established via gluing, duality, and mapping class group computations.