New Counterexamples to Knaster’s Conjecture
نویسنده
چکیده
Given a continuous map f : Sn−1 → Rm and n − m + 1 points p1, . . . , pn−m+1 ∈ Sn−1, does there exist a rotation % ∈ SO(n) such that f(%(p1)) = . . . = f(%(pn−m+1))? We give a negative answer to this question for m = 1 if n ∈ {61, 63, 65} or n ≥ 67 and for m = 2 if n ≥ 5.
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