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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A reimbedding algorithm for Casson handles

Author: Žarko Bižaca
Journal: Trans. Amer. Math. Soc. 345 (1994), 435-510
MSC: Primary 57N13; Secondary 57N55
MathSciNet review: 1236223
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Abstract: An algorithmic proof of Freedman's Reimbedding Theorem [F2] is given. This reimbedding algorithm produces an explicit description of an imbedded Casson tower with seven levels inside an arbitrary Casson tower with six levels. Our approach is similar to Freedman's original idea, but we also make essential use of the grope technology from [FQ]. The reimbedding algorithm is applied to obtain an explicitly described Casson handle inside an arbitrary six-level tower (Theorem A), a description of a family of exotic Casson handles (Theorem B) and an explicitly constructed exotic $ {\mathbb{R}^4}$.

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Keywords: Casson handles, Casson towers, exotic Casson handles, exotic $ {\mathbb{R}^4}$, reimbedding algorithm, Freedman's Reimbedding Theorem, capped gropes, Casson fingers, singular Norman trick
Article copyright: © Copyright 1994 American Mathematical Society