Vector fields and classical theorems of topology

  • Daniel Henry Gottlieb


The Author defines a new Index Theory in order to obtain new unified proof for some well known theorems (e.g. the Intermediate Value Theorem, Rouche's Theorem, The Gauss-Bonner Theorem, etc.) (Editor's abstract).


Vector Field Classical Theorem Vector Field Versus Jordan Curve Theorem Continuous Vector Field 


L'autore elabora una nuova Teoria dell'Indice mediante la quale ottiene nuove dimostrazioni in forma unificata di risultati classici (p.e. il teorema di valor medio, il teorema di Rouché. il teorema di Gauss-Bonnet ecc.) (Sunto dell'Editore).


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  1. [G1]Daniel H. Gottlieb,A certain subgroup of the fundamental group, Amer. J. Math., 87 (1966), pp. 1233–1237.Google Scholar
  2. [G2]Daniel H. Gottlieb.A de Moivre formula for fixed point theory, ATAS do 5o Encontro Brasiliero de Topologia Universidade de São Pavlo, São Carlos, S. P. Brasil, 31 (1988), pp. 59–67.Google Scholar
  3. [G3]Daniel H. Gottlieb,A de Moivre like formula for fixed point theory, Proceedings of the Fixed Point Theory Seminar at the 1986 International Congress of Mathematicians, R. F. Brown. (editor), Contemporary Mathematics, AMS Providence, Rhode Island, 72, pp. 99–106.Google Scholar
  4. [G4]Daniel H. Gottlieb,On the index of pullback vector fields, Proc. of the 2nd Siegen Topology Symposium, August 1987, Ulrick Koschorke (editor), Lecture Notes of Mathematics, Springer Verlag, New York.Google Scholar
  5. [G5]Daniel H. Gottlieb,Zeroes of pullback vector fields and fixed point theory for bodies, Algebraic topology, Proc. of Intl. Conference March 21–24, 1988, Contemporary Mathematics, 96, pp. 168–180.Google Scholar
  6. [G-S]Daniel H. Gottlieb andGeetha Samaranayake,The Index of Discontinuous Vector Fields (In Preparation).Google Scholar
  7. [HO1]Heinz Hopf,Über die Curvatura integra beschlossener Hyperflächen, Math. Ann., 95 (1925/26), pp. 340–367.CrossRefMathSciNetGoogle Scholar
  8. [HO2]Heinz Hopf,Vectorfelder in n-dimensionalin Mannigfatligkeiten, Math. Ann., 96 (1926/27), pp. 225–250.MATHCrossRefMathSciNetGoogle Scholar
  9. [Ha]Andre Haefliger,Quelques remarques sur les applications differentiables d'une surface dans le plan, Ann. Inst. Fourier, Grenoble 10 (1960), pp. 47–60.MATHMathSciNetGoogle Scholar
  10. [M]Marston Morse,Singular points of vector fields under general boundary conditions, Amer. J. Math., 51 (1929), pp. 165–178.CrossRefMathSciNetGoogle Scholar
  11. [P]Charles C. Pugh,A generalized Poincare index formula, Topology, 7 (1968), pp. 217–226.CrossRefMathSciNetGoogle Scholar
  12. [Sp]Michael Spivak,A Comprehensive Introduction to Differential Geometry, Publish or Perish, Inc., Wilmington, Delaware, 1979.Google Scholar
  13. [St]John Stallings Centerless Groups—An Algebraic Formulation of Gottlieb's Theorem, Topology, 4 (1965), pp. 129–134.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser-Verlag 1990

Authors and Affiliations

  • Daniel Henry Gottlieb
    • 1
  1. 1.Purdue UniversityPurdueItalia

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