Computable isomorphism invariants for the fundamental group of the complement of a plane projective curve
HTML articles powered by AMS MathViewer
- 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
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