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Minimal morse functions

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Global Analysis — Studies and Applications I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1108))

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References

  1. H. Bass. Algebraic K-theory, Benjamin, New-York, 1968.

    MATH  Google Scholar 

  2. O.I. Bogoyavlenskii. On exact function on manifold.-Mat.zametki, 8(1970), 77–83 (in Russian).

    MathSciNet  Google Scholar 

  3. M.Golubitsky, V.Guillemin. Stable mappings and their singularities Graduate text in Mathematics 14, Springer, 1973.

    Google Scholar 

  4. R.Lyndon, P.Schup. Combinatorial group theory. Ergebnisse der Mathematik und ihrer Grenzgebiete 69, Springer-Verlag, 1972.

    Google Scholar 

  5. J.Milnor. Morse theory. Princeton University Press, 1965.

    Google Scholar 

  6. J.Milnor. Lectures of the h-cobordism theorem. Princeton University Press, 1963.

    Google Scholar 

  7. J.Milnor. Introduction to algebraic K-theory. Princeton University Press, 1971.

    Google Scholar 

  8. S.P. Novikov. Many-valued functionals and functions. Analogy of Morse theory.-DAN SSSR, 260(1981), 31–34 (in Russian).

    Google Scholar 

  9. C.Rourrke, B.Sanderson. Introduction to picewise-linear topology. Ergebnise der Mathematik und ihre Grenzgebiete 69, Springer-Verlag 1972.

    Google Scholar 

  10. V.V.Sharko. Exact Morse functions. Preprint IM-75-9, Kiev, Institut matematiki AN Ukr.SSR, 1975 (in Russian).

    Google Scholar 

  11. V.V.Sharko. On smooth functions on manifolds. Preprint IM-79-22 Kiev, Institut matematiki AN Ukr.SSR, 1979 (in Russian).

    Google Scholar 

  12. V.V.Sharko. Minimal resolvents and Morse functions.-Doklady AN Ukr.SSR, ser.A, No 11 (1980), 31–33 (in Russian).

    Google Scholar 

  13. V.V.Sharko. On the equivalence of exact Morse functions.-Doklady AN Ukr.SSR, ser.A, No 12 (1980), 18–20 (in Russian).

    Google Scholar 

  14. V.V. Sharko. Stable algebra and Morse theory.-Ukr.mat.zhurnal, 32 (1980), 711–713 (in Russian).

    MathSciNet  MATH  Google Scholar 

  15. V.V. Sharko. Exact Morse functions on simply connected manifolds with not simply connected boundary.-Uspehi mat.nauk, 36 (1981), 205–206 (in Russian).

    MathSciNet  MATH  Google Scholar 

  16. M. Agoston. On handle decomposition and diffeomorphism.-Trans.AMS 198(1969), 21–26.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Alperin, K. Dennis, M. Stein. The non-triviality of SKI(Zn). Lecture Notes in Mathematics, Springer-Verlag, New York, 1973.

    Google Scholar 

  18. J. Andrews, Curtis M. Free group and handelbodies.-Proc.Amer.Math Soc., 16 (1965), 263–268.

    MathSciNet  Google Scholar 

  19. D.Barden. Structure of manifolds. Thesis, Cambridge University, 1963.

    Google Scholar 

  20. J. Cerf. Stratification naturelle des espaces de fonctions differentiables reeles et le theoreme de la pseudo-isotopie.-Publ.Math. I.E.H.S., 39 (1970), 3–280.

    Article  MATH  Google Scholar 

  21. A. Chenciner, F. Laudenbach. Contribution a une theorie de Smale a un parametre dans la cas non simplement connexe.-Ann.Scient.Ec. Norm.Sup., 3 (1970), 409–478.

    MathSciNet  MATH  Google Scholar 

  22. M. Cohen. A course in simple-homotopy theory. Graduate Text in Mathematics, Springer-Verlag, New York, 1973.

    Book  MATH  Google Scholar 

  23. H. Cohen. Whitehead torsion, group extension and Zeeman's conjecture in high dimensions.-Topology, 15 (1976), 79–88.

    MATH  Google Scholar 

  24. M. Dunwoody. The homotopy type of a two-dimensional complex.-Bul London, Math.Soc., 8 (1976), 218–229.

    Article  MathSciNet  MATH  Google Scholar 

  25. B.Hajduk. Comparing handle decompositions of homotopy equivalent manifolds.-Fund.Math., 95 (1977), No I.

    Google Scholar 

  26. B.Hajduk. Presentations of the fundamental group of manifolds.-Collq.Math., 1977.

    Google Scholar 

  27. H. Hatcher, J. Wagoner. Pseudo-isotopies of compact manifolds.-Asterisque, 6(1973), 3–274.

    MathSciNet  MATH  Google Scholar 

  28. T.Lam. Introduction theorem for Grotendieck groups and Whitehead groups of finite groups.-Ann.Sci.Ecole Norm.Sup., I (1968),No I.

    Google Scholar 

  29. R. Mandelbaum. Four-dimensional topology: an introduction.-Bul. Amer.Math.Soc., 2 (1980), 1–159.

    Article  MathSciNet  MATH  Google Scholar 

  30. M.Morse. The calculus of variations in the large. New York, 1934.

    Google Scholar 

  31. T. Matumoto. On the minimal ordered Morse functions on compact manifold.-Publ.RIMS, Kyoto Univ., 14 (1978), 673–684.

    Article  MathSciNet  MATH  Google Scholar 

  32. W. Metzler. Uber den homotopie Typ zweidiemensionaler CW-komplexe und elementar Transformationen bei Darstellung von Gruppen durch erceugende und defienierende Relationen.-J.rei.angew.Math.,285 (1976), 7–23.

    MathSciNet  Google Scholar 

  33. Algebraic and Geometric Topology.-Proc. of Sym. in Pure Math., 32 (1978), 311.

    Google Scholar 

  34. O.Rothaus. On the non-triviality of some group extensions given by generators and relations.-Ann. of Math. 106 (1977), No 3.

    Google Scholar 

  35. F. Sergereart. Un Theoreme de functions impsites sur cartains espaces de Frechet et quelqes applications.-Ann.Sci.Ecole Norm.Sup. 5 (1972), 599–660.

    MathSciNet  Google Scholar 

  36. S. Smale. Generalised Poincare's conjecture in dimensions greater then four.-Ann. of Math., 74 (1961), 391–406.

    Article  MathSciNet  MATH  Google Scholar 

  37. S. Smale. On the structure of manifolds.-Amer.J.Math., 84 (1962) 387–399.

    Article  MathSciNet  MATH  Google Scholar 

  38. M.Stein. Whitehead groups of finite groups.-Bul.Amer.Math.Soc., 84 (1978), No 2.

    Google Scholar 

  39. M. Shub, D. Sullivan. Homology theory and Dynamical Systems.-Topology, 14 (1975), 109–132.

    Article  MathSciNet  MATH  Google Scholar 

  40. J.Webb. The minimal relation modules of a finite abelian group.-J. of Pure and Appl.Algebra, 21 (1981), No 2.

    Google Scholar 

  41. P. Wright, Group presentations and formal deformations.-Trans. Amer.Math.Soc., 1975, 208, 161–169.

    Article  MathSciNet  MATH  Google Scholar 

  42. H. Hendrics. La stratification naturelle de espace des functions differentiables reeles ne est pas la bonne.-C.R.Acad.Sci., Paric, 244 (1972), 618–620.

    Google Scholar 

  43. I.A. Volodin. Generalized Whitehead groups and pseudoisotopics.-Uspehi mat.nauk, 27 (1972), 229–230 (in Russian).

    MathSciNet  Google Scholar 

  44. E. Zeeman. On the dunce hat.-Topology, 2 (1964), 341–358.

    Article  MathSciNet  MATH  Google Scholar 

  45. M.Maller. Thesis. University of Warwick, 1978.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Uk.SSR, 252601, Kiev, USSR

    V. V. Sharko

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  1. V. V. Sharko
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Yurii G. Borisovich Yurii E. Gliklikh A. M. Vershik

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© 1984 Springer-Verlag

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Sharko, V.V. (1984). Minimal morse functions. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications I. Lecture Notes in Mathematics, vol 1108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099560

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  • DOI: https://doi.org/10.1007/BFb0099560

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13910-2

  • Online ISBN: 978-3-540-39132-6

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