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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Simplicial triangulation of noncombinatorial manifolds of dimension less than $ 9$


Author: Martin Scharlemann
Journal: Trans. Amer. Math. Soc. 219 (1976), 269-287
MSC: Primary 57D05; Secondary 57C15
MathSciNet review: 0415629
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Abstract: Necessary and sufficient conditions are given for the simplicial triangulation of all noncombinatorial manifolds in the dimension range $ 5 \leqslant n \leqslant 7$, for which the integral Bockstein of the combinatorial triangulation obstruction is trivial. A weaker theorem is proven in case $ n = 8$.

The appendix contains a proof that a map between PL manifolds which is a TOP fiber bundle can be made a PL fiber bundle.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0415629-5
PII: S 0002-9947(1976)0415629-5
Keywords: Noncombinatorial triangulation, PL triangulation obstruction, integral Bockstein homomorphism, manifold category (DIFF, TOP, PL)
Article copyright: © Copyright 1976 American Mathematical Society