Skip to main content

Part of the book series: Kluwer Texts in the Mathematical Sciences ((TMS,volume 9))

  • 1193 Accesses

Abstract

In the previous chapters, we considered general properties of topological spaces and their mappings. However, in topology and its applications there appear spaces with additional structures, e.g., smooth manifolds and fibre bundles which are of great importance in many branches of modern mathematics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Review of the Recommended Literature

  1. Golubitzky M., Guillemin V., Stable Mappings and Their Singularities, Springer, New York, 1974.

    Google Scholar 

  2. Dubrovin B. A., Novikov S. P., and Fomenko A. T., Modern Geometry: Methods and Applications, Nauka, Moscow, 1986, 760 pp. (Russian); English translation, Springer, 1984, 1987.

    Google Scholar 

  3. Milnor J, Stasheff J., Characteristic Classes, Princeton Univ. Press, Princeton, 1974.

    MATH  Google Scholar 

  4. Mischenko A. S., Vector bundles and their applications,Nauka, Moscow, 1984, 208 pp. (Russian)

    Google Scholar 

  5. Mischenko A. S., Fomenko A. T., A course of Differential Geometry and Topology,MGU, Moscow, 1980, 439 pp. (Russian)

    Google Scholar 

  6. Narasimhan R., Analysis on Real and Complex Manifolds, Masson & Cie, Editeur. North-Holland Publ. Comp., Paris, Amsterdam, 1968.

    Google Scholar 

  7. Novikov C. P., Fomenko A. T., Elements of Differential Geometry and Topology, Nauka, Moscow, 1987, 432 pp. (Russian); English translation, Kluwer Acad. Publishers, 1990.

    Google Scholar 

  8. Pontryagin L. S., Smooth Manifolds and Their Application to Homotopy Theory,Nauka, Moscow, 1985, 174 pp. (Russian)

    Google Scholar 

  9. Postnikov M. M., Intorduction to Morse Theory,Nauka, Moscow, 1971, 568 pp. (Russian)

    Google Scholar 

  10. Postnikov M. M., Lectures on Geometry. Semester III. Smooth Manifolds,Nauka, Moscow, 1987, 480 pp. (Russian)

    Google Scholar 

  11. Rohlin V. A., Fuks D. B, First Course of Topology. Geometric Chapters,Nauka, Moscow, 1977, 488 pp. (Russian)

    Google Scholar 

  12. Steenrod N., The Topology of Fibre Bundles, Princeton Univ. Press, Princeton, 1951.

    MATH  Google Scholar 

  13. Sternberg S, Lectures on Differential Geometry, Prentice Hall, Englewood Cliffs, NJ., 1964.

    Google Scholar 

  14. Teleman c., Elemente de Topologie si Variei Differentiable, Bucharest, 1964. ( Romanian )

    Google Scholar 

  15. Warner F., Foundations of Differentiable Manifolds and Lie Groups,Springer Verlag, 1983.

    Google Scholar 

  16. Hirsch M. W., Differential Topology, Springer-Verlag, New York-Berlin-Heidelberg, 1976.

    Book  MATH  Google Scholar 

  17. Hu S.-T., Homotopy Theory, Academic press, New York-London, 1959.

    MATH  Google Scholar 

  18. Husemoller D., Fibre Bundles, MacGraw-Hill, 1975.

    Google Scholar 

  19. Chernaysky A. V., Matveyev S. V., Outline of Topology of Manifolds,MOU, Krasnodar, 1974, 176 pp. (Russian)

    Google Scholar 

  20. Boltyansky V. G., Efremovich V. A., Visual Topology,Nauka, Moscow, 1983, 160 pp. (Russian)

    Google Scholar 

  21. Milnor J., Weaver D. W., Topology from the differentiable viewpoint, Univ. Pr. of Virginia, 1969.

    Google Scholar 

  22. Novikov C. P., Topology,Sovr. Probl. Matematiki. Fund. Napravleniya 12 (1986), VINITI AN USSR, 5–252. (Russian)

    Google Scholar 

  23. Mischenko A. S., Solovyev Yu. P., and Fomenko A. T., Problems in Differential Geometry and Topology,MGU, Moscow, 1981, 183 pp. (Russian)

    Google Scholar 

  24. Novikov C. P., Mishchenko A. S., Solovyev Yu. P., and Fomenko A. T., Problems in Geometry. Differential Geometry and Topology,MGU, Moscow, 1978, 164 pp. (Russian)

    Google Scholar 

  25. Dieudonné J., Foundations of Modern Analysis, Academic Press, New York, 1969.

    Google Scholar 

  26. Kudryavtsev L. D., Mathematical Analysis Vol I, H, Vysshaya Shkola, Moscow, 1981, 1 687 pp., 2 584 pp. (Russian)

    Google Scholar 

  27. Fomenko A. T., Differential Geometry and Topology. Additional chapters,MGU, Moscow, 1983, 216 pp. (Russian)

    Google Scholar 

  28. Fomenko A. T., Variational Problems in Topology, MGU, Moscow, 1984, 216 pp. (Russian); English translation, Kluwer Acad. Publishers, 1990.

    Google Scholar 

  29. Seifert H., Trelfall V., Lehrbruch der Topologie, Shelsea reprint, 1968; Originally: Teubor, 1934.

    Google Scholar 

  30. Rohlin V. A., Fuks D. B, First Course of Topology. Geometric Chapters,Nauka, Moscow, 1977, 488 pp. (Russian)

    Google Scholar 

  31. Pontryagin L. S., Continuous Groups,Nauka, Moscow, 1984, 520 pp. (Russian)

    Google Scholar 

  32. Massey W., Stallings J., Algebraic Topology. Introduction,Mir, Moscow, 1977, 278 pp. (Russian)

    Google Scholar 

  33. Springer G., Introduction to Riemann Surfaces, Addison-Wesley, Reading, 1957.

    MATH  Google Scholar 

  34. Forster O., Riemannsche Flächen, Springer-Verlag, Heidelberg, 1979.

    Google Scholar 

  35. Milnor J., Morse Theory, Princeton Univ. Press, Princeton, 1963.

    MATH  Google Scholar 

  36. Arnold V. I., Mathematical Methods in Classical Mechanics,Nauka, Moscow, 1979, 432 pp. (Russian); English translation.

    Google Scholar 

  37. Arnold V. I., Ordinary Differential Equations,Nauka, Moscow, 1984, 272 pp. (Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Borisovich, Y.G., Bliznyakov, N.M., Fomenko, T.N., Izrailevich, Y.A. (1995). Manifolds and Fiberings. In: Introduction to Differential and Algebraic Topology. Kluwer Texts in the Mathematical Sciences, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1959-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-1959-9_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4558-4

  • Online ISBN: 978-94-017-1959-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics