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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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Computable isomorphism invariants for the fundamental group of the complement of a plane projective curve
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by Edward M. Arnold PDF
Proc. Amer. Math. Soc. 71 (1978), 345-350 Request permission

Abstract:

The aim of this paper is to attach computable isomorphism invariants to the fundamental groups ${\pi _1}({{\mathbf {P}}^2} - c)$ where c is an irreducible plane projective curve. We use these invariants to distinguish certain of these groups. The vehicle used to obtain these invariants is the free differential calculus of R. Fox.
References
    E. M. Arnold, Computable isomorphism invariants for the fundamental group of the complement of a plane projective curve, Ph.D. Thesis, Univ. of Washington, Spokane, 1975.
  • Denis Cheniot, Le théorème de Van Kampen sur le groupe fondamental du complémentaire d’une courbe algébrique projective plane, Fonctions de plusieurs variables complexes (Sém. François Norguet, à la mémoire d’André Martineau), Lecture Notes in Math., Vol. 409, Springer, Berlin, 1974, pp. 394–417 (French). MR 0369370
  • Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Ginn and Company, Boston, Mass., 1963. Based upon lectures given at Haverford College under the Philips Lecture Program. MR 0146828
  • Ralph H. Fox, Free differential calculus. II. The isomorphism problem of groups, Ann. of Math. (2) 59 (1954), 196–210. MR 62125, DOI 10.2307/1969686
  • Michael O. Rabin, Recursive unsolvability of group theoretic problems, Ann. of Math. (2) 67 (1958), 172–194. MR 110743, DOI 10.2307/1969933
  • Oscar Zariski, On the Problem of Existence of Algebraic Functions of Two Variables Possessing a Given Branch Curve, Amer. J. Math. 51 (1929), no. 2, 305–328. MR 1506719, DOI 10.2307/2370712
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 345-350
  • MSC: Primary 14H30; Secondary 14B05, 55A05
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0485885-3
  • MathSciNet review: 0485885