Abstract
We classify simple singularities of functions on space curves. We show that their bifurcation sets have the same properties as those of functions on smooth manifolds and complete intersections [3, 4]: thek(π, 1)-theorem for the bifurcation diagram of functions is true, and both this diagram and the discriminant are saito's free divisors.
This is a preview of subscription content, log in via an institution to check access.
References
V. I. Arnold, Usp. Mat. Nauk,29, No. 3, 243–244 (1974).
V. I. Arnold, V. V. Goryunov, O. V. Lyashko, and V. A. Vassiliev, Singularities I. Local and Global Theory, Encyclopaedia of Mathematical Sciences, Vol. 6. Dynamical Systems VI Springer-Verlag, Berlin a.o., 1993.
V. I. Arnold, V. V. Goryunov, O. V. Lyashko, and V. A. Vassiliev, Singularities II. Classification and Applications, Encyclopaedia of Mathematical Sciences, Vol. 39, Dynamical Systems VIII, Springer-Verlag, Berlin a.o., 1993.
V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps. Vol. II. Monodromy and Asymptotics of Integrals, Monographs in Mathematics, Vol. 83, Birkhäuser, Boston, MA, 1988.
J. W. Bruce, Bull. London Math. Soc.,17, No. 5, 257–262 (1985).
J. N. Damon, Mem. Amer. Math. Soc.,50, No. 306, 1–88 (1984).
V. V. Goryunov, Funkts. Anal. Prilozhen.,15, No. 2, 1–8 (1981).
A. Frühbis-Krueger, Preprint, Universität Kaiserslautern, 1998.
E. J. N. Looijenga, Invent. Math.,23, 105–116 (1974).
V. M. Zakalyukin, Funkts. Anal. Prilozhen.,10, No. 2, 69–70 (1976).
Additional information
Department of Mathematical Sciences Division of Pure Mathematics, The University of Liverpool. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol, 34, No. 2, pp. 63–67, April–June, 2000.
Translated by V. V. Goryunov
Rights and permissions
About this article
Cite this article
Goryunov, V.V. Simple functions on space curves. Funct Anal Its Appl 34, 129–132 (2000). https://doi.org/10.1007/BF02482426
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02482426