A Solution to De Groot’s Absolute Cone Conjecture
نویسنده
چکیده
A compactum X is an ‘absolute cone’ if, for each of its points x, the space X is homeomorphic to a cone with x corresponding to the cone point. In 1971, J. de Groot conjectured that each n-dimensional absolute cone is an n-cell. In this paper, we give a complete solution to that conjecture. In particular, we show that the conjecture is true for n ≤ 3 and false for n ≥ 5. For n = 4, the absolute cone conjecture is true if and only if the 3-dimensional Poincaré Conjecture is true.
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تاریخ انتشار 2005