Bounds on homotopy connectivity of Čech complexes of spheres are derived from coverings, proving the homotopy type changes infinitely many times with scale r in (0, π) for n ≥ 1.
A short proof of Kneser’s conjecture.Journal of Combinatorial Theory, Series A , 25(3):325–326, 1978
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Homotopy connectivity of \v{C}ech complexes of spheres
Bounds on homotopy connectivity of Čech complexes of spheres are derived from coverings, proving the homotopy type changes infinitely many times with scale r in (0, π) for n ≥ 1.