德格鲁特绝对锥猜想的解

Topology Pub Date : 2007-03-01 DOI:10.1016/j.top.2006.12.001

Craig R. Guilbault

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引用次数: 7

摘要

一个紧致X是一个“绝对锥”，如果对于它的每一个点X，空间X同胚于一个锥，其中X对应于锥点。1971年，J. de Groot推测每个n维绝对锥都是一个n细胞。本文给出了该猜想的完全解。特别地，我们证明了当n≤3时该猜想为真，当n≥5时该猜想为假。对于n=4，当且仅当三维庞加莱猜想为真，绝对锥猜想为真。

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A solution to de Groot’s absolute cone conjecture

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 $n \leq 3$ and false for $n \geq 5$ . For $n = 4$ , the absolute cone conjecture is true if and only if the 3-dimensional Poincaré Conjecture is true.

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来源期刊

Topology 数学-数学

自引率

0.00%

发文量

审稿时长

1 months