Literature Cited
M. Gromov, Partial Differential Relations, Springer, Berlin a.o. (1986).
J. Cerf, "La stratification naturelle des espaces de fonctions et le theoreme de la pseudoisotopie," Publ. Math. IHES,39, 6–173 (1971).
V. V. Sharko, "Minimal Morse functions," in: Geometry and Topology in Global Nonlinear Problems [in Russian], Voronezh (1984), pp. 123–144.
K. Igusa, "Higher singularities of smooth functions are unnecessary," Ann. Math.,119, 1–58 (1984).
J. Cerf, "Suppression des singularities de codimension plus grande que 1 dans les familles de fonctions differentiables reeles (d'apres K. Igusa)," Semin. Bourbaki-1983, No. 627 (1984).
V. I. Arnol'd, V. A. Vasil'ev, V. V. Goryunov, and O. V. Lyashko, Singularities [in Russian], VINITI, Moscow (1988).
V. I. Arnol'd, "Spaces of functions with moderate singularities," Funktsion. Anal. Prilozhen.,23, No. 3, 1–10 (1989).
K. Igusa, "On the homotopy type of the space of generalized Morse functions," Topology,23, No. 2, 245–256 (1984).
K. Igusa, "The space of framed functions," Trans. Am. Math. Soc.,301, No. 2 (1987).
M. Golubitsky and V. Guillemin, Stable Maps and Their Singularities [Russian translation], Mir, Moscow (1977).
D. B. Fuks, A. T. Fomenko, and V. L. Gutenmakher, Homotopic Topology [in Russian], Moscow State Univ. (1969).
E. Dyer and R. K. Lashof, "Homology of iterated loop spaces," Am. J. Math.,84, No. 1, 35–83 (1962).
V. A. Vasil'ev, "Stable cohomology of complements to discriminants," Itogi Nauki Tekhn. Seriya Sovremennye Problemy Matematiki [in Russian], Vol. 33, VINITI, Moscow (1988), pp. 3–29.
J. Milnor, The h-Cobordism Theorem [Russian translation], Mir, Moscow (1969).
V. A. Rokhlin and D. B. Fuks, Beginning Course in Topology [in Russian], Nauka, Moscow (1977).
S. Smale, "On the structure of manifolds," Matematika (Collection of Russian translations),8, No. 4, 95–108 (1964).
V. A. Vassilyev, Lagrange and Legendre Characteristic Classes, Gordon and Breach, New York (1988).
Additional information
Institute of Applied Mathematics, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 23, No. 4, pp. 24–36, October–December, 1989.
Rights and permissions
About this article
Cite this article
Vasil'ev, V.A. Topology of spaces of functions without compound singularities. Funct Anal Its Appl 23, 277–286 (1989). https://doi.org/10.1007/BF01078942
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01078942