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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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The inverse limit of the fundamental groups of branched cyclic coverings
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by Michael Dellomo PDF
Proc. Amer. Math. Soc. 104 (1988), 321-326 Request permission

Abstract:

Cowsik and Swarup [CS] have shown that the homology groups of the infinite cyclic cover of a knot inject into the inverse limit of the homology groups of the branched cyclic covers. They also give conditions under which the injection is an isomorphism. We prove an analogous result for the fundamental group and generalize it to the case of links.
References
    A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, Berlin and New York, 1972. G. Burde and H. Zieschang, Eine Kennzeichnung der Torus Knoten, Math. Ann. 167 (1966), 169-176. R. C. Cowsik and G. A. Swarup, A remark on infinite cyclic covers, J. Pure Appl. Algebra 11 (1977), 131-138. M. Dellomo, On the inverse limit of the finite branched cyclic covers of a knot, J. Pure Appl. Algebra 40 (1986), 15-26. —, Through the non-simply connected looking glass, or the inverse limit of finite branched covers, Ph.D. Thesis, Johns Hopkins Univ., 1984. J. Dydak and J. Segal, Shape theory: An introduction, Lecture Notes in Math., vol. 688, Springer-Verlag, Berlin, 1978. J. Hempel, Residual finiteness for $3$-manifolds, Ann. of Math. Studies (to appear). W. Magnus, A. Karras and D. Solitar, Combinatorial group theory, Dover, New York, 1976.
  • Sibe Mardešić and Jack Segal, Shape theory, North-Holland Mathematical Library, vol. 26, North-Holland Publishing Co., Amsterdam-New York, 1982. The inverse system approach. MR 676973
  • Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 104 (1988), 321-326
  • MSC: Primary 57M25; Secondary 55P25
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0958092-1
  • MathSciNet review: 958092