A reimbedding algorithm for Casson handles

Bižaca, Žarko

doi:10.1090/S0002-9947-1994-1236223-3

A reimbedding algorithm for Casson handles
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by Žarko Bižaca

Trans. Amer. Math. Soc. 345 (1994), 435-510

DOI: https://doi.org/10.1090/S0002-9947-1994-1236223-3

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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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