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Lefschetz duality and topological tubular neighbourhoods


Author: F. E. A. Johnson
Journal: Trans. Amer. Math. Soc. 172 (1972), 95-110
MSC: Primary 57A45; Secondary 57A35
DOI: https://doi.org/10.1090/S0002-9947-1972-0310892-X
MathSciNet review: 0310892
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Abstract: We seek an analogue for topological manifolds of closed tubular neighbourhoods (for smooth imbeddings) and closed regular neighbourhoods (for piecewise linear imbeddings). We succeed when the dimension of the ambient manifold is at least six. The proof uses topological handle theory, the results of Siebenmann's thesis, and a strong version of the Lefschetz Duality Theorem which yields a duality formula for Wall's finiteness obstruction.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0310892-X
Keywords: Class of closed neighbourhoods, derived category, finiteness obstruction, Lefschetz Duality Theorem, collar neighbourhood, topological handle theory, stable end, Siebenmann thesis
Article copyright: © Copyright 1972 American Mathematical Society

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