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1998 | 45 | 1 | 25-39
Tytuł artykułu

The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
Rocznik
Tom
45
Numer
1
Strony
25-39
Opis fizyczny
Daty
wydano
1998
Twórcy
autor
  • Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada
  • Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada
Bibliografia
  • [1] J. Bryden, C. Hayat-Legrand, H. Zieschang and P. Zvengrowski, L'anneau de cohomologie d'une variété de Seifert, C. R. Acad. Sci. Paris 324, Sér. I (1997), 323-326.
  • [2] J. Bryden, C. Hayat-Legrand, H. Zieschang and P. Zvengrowski, The cohomology ring of a class of Seifert manifolds, Top. and its Appl., to appear.
  • [3] J. Bryden and P. Zvengrowski, The cohomology ring of the orientable Seifert manifolds II, preprint.
  • [4] S. Eilenberg and T. Ganea, On the Lusternik-Schnirelmann category of abstract groups, Ann. of Math. 65 (1957), 517-518.
  • [5] R. H. Fox, Free differential calculus. I. Derivations in the free group ring, Ann. of Math. 57 (1953), 547-560.
  • [6] R. H. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. 42 (1941), 333-370.
  • [7] C. Hayat-Legrand, S. Wang and H. Zieschang, Degree-one maps onto lens spaces, Pac. J. Math. 176 (1996), 19-32.
  • [8] J. Hempel, 3-Manifolds, Annals of Math. Studies, vol. 86, Princeton University Press, Princeton, New Jersey 1976, 115-135.
  • [9] N. Iwase, Ganea's conjecture on Lusternik-Schnirelmann category, preprint.
  • [10] I. M. James, On category, in the sense of Lusternik-Schnirelmann, Topology 17 (1978), 331-348.
  • [11] S. MacLane, Homology, Springer-Verlag, Berlin, 1963.
  • [12] J. M. Montesinos, Classical Tesselations and Three-Manifolds, Springer-Verlag, Berlin, 1987.
  • [13] P. Orlik, Seifert Manifolds, Lecture Notes in Math. 291, Springer-Verlag, Berlin, 1972.
  • [14] K. Reidemeister, Homotopieringe und Linsenräume, Abh. Math. Sem. Univ. Hamburg 11 (1935), 102-109.
  • [15] Y. B. Rudyak, On category weight and its applications, preprint.
  • [16] P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 No. 56 (1983), 401-487.
  • [17] H. Seifert, Topologie dreidimensionaler gefaserter Räume, Acta Math. 60 (1932), 147-238.
  • [18] H. Seifert and W. Threlfall, A Textbook of Topology, Academic Press, 1980.
  • [19] A. R. Shastri, J. G. Williams and P. Zvengrowski, Kinks in general relativity, International Journal of Theoretical Physics 19 (1980), 1-23.
  • [20] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
  • [21] N. Steenrod and D. B. A. Epstein, Cohomology Operations, The University of Princeton Press, Princeton, N.J., 1962.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv45i1p25bwm
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