Bing Topology & Casson Handles
نویسنده
چکیده
In 1914, the 1-dimensional case of the conjecture was proven in full generality by Caratheodory and Osgood-Taylor using elaborate methods from complex analysis. The 2-dimensional case was studied in the 1920s by Alexander who first circulated a manuscript claiming a proof but soon discovered a counterexample himself, the famous horned sphere. Later Alexander found an extra condition under which the Schoenflies conjecture holds in dimension 2. This extra condition is known as flatness and makes sense in arbitrary dimensions. It means that the embedding of S extends to an embedding of S × [−1, 1] in which S sits as S × 0. In the next 40 years almost no progress was made which lead to much dismay about the topological category until Mazur gave his argument.
منابع مشابه
ASD moduli spaces over four–manifolds with tree-like ends
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