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Vector fields and classical theorems of topology

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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).

Abstract

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).

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References

  • [G1]Daniel H. Gottlieb,A certain subgroup of the fundamental group, Amer. J. Math., 87 (1966), pp. 1233–1237.

    Google Scholar 

  • [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 

  • [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.

  • [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.

  • [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.

  • [G-S]Daniel H. Gottlieb andGeetha Samaranayake,The Index of Discontinuous Vector Fields (In Preparation).

  • [HO1]Heinz Hopf,Über die Curvatura integra beschlossener Hyperflächen, Math. Ann., 95 (1925/26), pp. 340–367.

    Article  MathSciNet  Google Scholar 

  • [HO2]Heinz Hopf,Vectorfelder in n-dimensionalin Mannigfatligkeiten, Math. Ann., 96 (1926/27), pp. 225–250.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ha]Andre Haefliger,Quelques remarques sur les applications differentiables d'une surface dans le plan, Ann. Inst. Fourier, Grenoble 10 (1960), pp. 47–60.

    MATH  MathSciNet  Google Scholar 

  • [M]Marston Morse,Singular points of vector fields under general boundary conditions, Amer. J. Math., 51 (1929), pp. 165–178.

    Article  MathSciNet  Google Scholar 

  • [P]Charles C. Pugh,A generalized Poincare index formula, Topology, 7 (1968), pp. 217–226.

    Article  MathSciNet  Google Scholar 

  • [Sp]Michael Spivak,A Comprehensive Introduction to Differential Geometry, Publish or Perish, Inc., Wilmington, Delaware, 1979.

    Google Scholar 

  • [St]John Stallings Centerless Groups—An Algebraic Formulation of Gottlieb's Theorem, Topology, 4 (1965), pp. 129–134.

    Article  MATH  MathSciNet  Google Scholar 

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(Conferenza tenuta il 24 giugno 1991)

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Gottlieb, D.H. Vector fields and classical theorems of topology. Seminario Mat. e. Fis. di Milano 60, 193–203 (1990). https://doi.org/10.1007/BF02925086

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