manuscripta mathematica

, Volume 95, Issue 3, pp 289–294 | Cite as

The Lyusternik–Shnirel'man category,¶vector bundles, and immersions of manifolds

  • Július Korbaš
  • András Szűcs


One of our two main results exhibits for a vector bundle over a compact Hausdorff space X an interplay between its span, its possible splittings, and the Lyusternik–Shnirel'man category of X. The other main result, also on vector bundles and the Lyusternik–Shnirel'man category, enables us to derive certain inequalities connecting the immersion codimension, the stable span, and the Lyusternik–Shnirel'man category of a smooth closed manifold which is not stably parallelizable. Our results are applicable in various situations of general interest.

Mathematics Subject Classification (1991): Primary 55M30, 55R25; Secondary 57R25, 57R42, 55R10 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Július Korbaš
    • 1
  • András Szűcs
    • 2
  1. 1.Department of Algebra, Faculty of Mathematics and Physics, Comenius University,¶Mlynská dolina, SK-842 15 Bratislava, Slovakia. e-mail: korbas@fmph.uniba.skSK
  2. 2.Department of Analysis, Eötvös Loránd University, Müzeum krt. 6–8, H-1080 Budapest, Hungary. e-mail: szucsandras@ludens.elte.huHU

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