A solution to de Groot's absolute cone conjecture

Craig R. Guilbault

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A solution to de Groot's absolute cone conjecture

Craig R. Guilbault

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Abstract

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<4 and false for n>4. For n=4, the absolute cone conjecture is true if and only if the 3-dimensional Poincare Conjecture is true.

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BibTeX RIS

Craig R. Guilbault. 2005-07-19. A solution to de Groot's absolute cone conjecture. https://arxiv.org/abs/math/0507395

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