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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
DOI: https://doi.org/10.1090/S0002-9939-1978-0485885-3
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?)

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  • [3] R. H. Crowell and R. H. Fox, Introduction to knot theory, Ginn, Boston, Mass., 1962. MR 0146828 (26:4348)
  • [4] R. H. Fox, Free differential calculus. II. The isomorphism problem of groups, Ann. of Math. (2) 59 (1954), 196-210. MR 0062125 (15:931e)
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  • [6] O. Zariski, On the existence of algebraic functions of two variables possessing a given branch curve, Amer. J. Math. 51 (1929), 305-328. MR 1506719

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Additional Information

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

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