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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A handlebody with one pillbox has no fake $3$-cells
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by J. O. Berge and Matthew G. Brin PDF
Proc. Amer. Math. Soc. 52 (1975), 390-392 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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