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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A handlebody with one pillbox has no fake $ 3$-cells


Authors: J. O. Berge and Matthew G. Brin
Journal: Proc. Amer. Math. Soc. 52 (1975), 390-392
MSC: Primary 57A10
DOI: https://doi.org/10.1090/S0002-9939-1975-0375317-5
MathSciNet review: 0375317
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Abstract: The main result establishes upper bounds on the rank of $ {H_1}$ of orientable $ 3$-manifolds with fake $ 3$-cells and on the rank of $ {\pi _1}$ of closed orientable $ 3$-manifolds with fake $ 3$-cells. As a consequence we get that a $ 3$-manifold obtained by sewing one pillbox on a handlebody of arbitrary genus cannot contain a fake $ 3$-cell.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0375317-5
Keywords: $ 3$-manifold, homotopy $ 3$-sphere, Heegaard splitting, handlebody, first homology, fundamental group
Article copyright: © Copyright 1975 American Mathematical Society