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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Homotopical variations and high-dimensional Zariski-van Kampen theorems
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by D. Chéniot and C. Eyral PDF
Trans. Amer. Math. Soc. 358 (2006), 1-10 Request permission


We give a new definition of the homotopical variation operators occurring in a recent high-dimensional Zariski-van Kampen theorem, a definition which opens the way to further generalizations of theorems of this kind.
  • V. I. Arnol′d, S. M. Guseĭn-Zade, and A. N. Varchenko, Singularities of differentiable maps. Vol. II, Monographs in Mathematics, vol. 83, Birkhäuser Boston, Inc., Boston, MA, 1988. Monodromy and asymptotics of integrals; Translated from the Russian by Hugh Porteous; Translation revised by the authors and James Montaldi. MR 966191, DOI 10.1007/978-1-4612-3940-6
  • D. Cheniot, Une démonstration du théorème de Zariski sur les sections hyperplanes d’une hypersurface projective et du théorème de Van Kampen sur le groupe fondamental du complémentaire d’une courbe projective plane, Compositio Math. 27 (1973), 141–158 (French). MR 366922
  • Denis Chéniot, Topologie du complémentaire d’un ensemble algébrique projectif, Enseign. Math. (2) 37 (1991), no. 3-4, 293–402 (French). MR 1151752
  • D. Chéniot, Vanishing cycles in a pencil of hyperplane sections of a non-singular quasi-projective variety, Proc. London Math. Soc. (3) 72 (1996), no. 3, 515–544. MR 1376767, DOI 10.1112/plms/s3-72.3.515
  • D. Chéniot and A. Libgober, Zariski-van Kampen theorem for higher-homotopy groups, J. Inst. Math. Jussieu 2 (2003), no. 4, 495–527. MR 2006797, DOI 10.1017/S1474748003000148
  • Mark Goresky and Robert MacPherson, Stratified Morse theory, Singularities, Part 1 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, R.I., 1983, pp. 517–533. MR 713089
  • Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR 932724, DOI 10.1007/978-3-642-71714-7
  • Helmut A. Hamm and Lê Dũng Tráng, Lefschetz theorems on quasiprojective varieties, Bull. Soc. Math. France 113 (1985), no. 2, 123–142 (English, with French summary). MR 820315
  • P. J. Hilton and S. Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. MR 0115161
  • Lê Dũng Tráng and B. Teissier, Cycles evanescents, sections planes et conditions de Whitney. II, Singularities, Part 2 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 65–103 (French, with English summary). MR 713238
  • A. Libgober, Homotopy groups of the complements to singular hypersurfaces. II, Ann. of Math. (2) 139 (1994), no. 1, 117–144. MR 1259366, DOI 10.2307/2946629
  • William S. Massey, A basic course in algebraic topology, Graduate Texts in Mathematics, vol. 127, Springer-Verlag, New York, 1991. MR 1095046
  • Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
  • Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258
  • E.R. van Kampen, “On the fundamental group of an algebraic curve”, Amer. J. Math. 55 (1933) 255–260.
  • Hassler Whitney, Tangents to an analytic variety, Ann. of Math. (2) 81 (1965), 496–549. MR 192520, DOI 10.2307/1970400
  • O. Zariski, “On the problem of existence of algebraic functions of two variables possessing a given branch curve”, Amer. J. Math. 51 (1929) 305–328.
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Additional Information
  • D. Chéniot
  • Affiliation: LATP, URA CNRS 225, Centre de Mathématiques et Informatique, Université de Provence, 39 rue F. Joliot-Curie, 13453 Marseille cédex 13, France
  • C. Eyral
  • Affiliation: Department of Mathematics, The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
  • Received by editor(s): December 9, 2002
  • Published electronically: August 25, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 1-10
  • MSC (2000): Primary 14F35; Secondary 14D05, 32S50, 55Q99
  • DOI:
  • MathSciNet review: 2171220