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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Computable isomorphism invariants for the fundamental group of the complement of a plane projective curve


Author: Edward M. Arnold
Journal: Proc. Amer. Math. Soc. 71 (1978), 345-350
MSC: Primary 14H30; Secondary 14B05, 55A05
MathSciNet review: 0485885
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] 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), Springer, Berlin, 1974, pp. 394–417. Lecture Notes in Math., Vol. 409 (French). MR 0369370 (51 #5603)
  • [3] Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Based upon lectures given at Haverford College under the Philips Lecture Program, Ginn and Co., Boston, Mass., 1963. MR 0146828 (26 #4348)
  • [4] Ralph H. Fox, Free differential calculus. II. The isomorphism problem of groups, Ann. of Math. (2) 59 (1954), 196–210. MR 0062125 (15,931e)
  • [5] Michael O. Rabin, Recursive unsolvability of group theoretic problems, Ann. of Math. (2) 67 (1958), 172–194. MR 0110743 (22 #1611)
  • [6] 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, http://dx.doi.org/10.2307/2370712

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0485885-3
PII: S 0002-9939(1978)0485885-3
Keywords: Isomorphism invariants, free differential calculus, plane projective cure, singular curve, fundamental group
Article copyright: © Copyright 1978 American Mathematical Society