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

J. Bryden; P. Zvengrowski

Banach Center Publications (1998)

  • Volume: 45, Issue: 1, page 25-39
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Bryden, J., and Zvengrowski, P.. "The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category." Banach Center Publications 45.1 (1998): 25-39. <http://eudml.org/doc/208907>.

@article{Bryden1998,
abstract = {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.},
author = {Bryden, J., Zvengrowski, P.},
journal = {Banach Center Publications},
keywords = {cup products; cup product length; Lusternik-Schnirelmann category; degree one maps; diagonal map; Seifert manifolds; cohomology algebra; Seifert manifold; Lyusternik-Shnirel'man category},
language = {eng},
number = {1},
pages = {25-39},
title = {The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category},
url = {http://eudml.org/doc/208907},
volume = {45},
year = {1998},
}

TY - JOUR
AU - Bryden, J.
AU - Zvengrowski, P.
TI - The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category
JO - Banach Center Publications
PY - 1998
VL - 45
IS - 1
SP - 25
EP - 39
AB - 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.
LA - eng
KW - cup products; cup product length; Lusternik-Schnirelmann category; degree one maps; diagonal map; Seifert manifolds; cohomology algebra; Seifert manifold; Lyusternik-Shnirel'man category
UR - http://eudml.org/doc/208907
ER -

References

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  1. [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. [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. Zbl0964.57019
  3. [3] J. Bryden and P. Zvengrowski, The cohomology ring of the orientable Seifert manifolds II, preprint. Zbl1025.57031
  4. [4] S. Eilenberg and T. Ganea, On the Lusternik-Schnirelmann category of abstract groups, Ann. of Math. 65 (1957), 517-518. Zbl0079.25401
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  16. [16] P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 No. 56 (1983), 401-487. Zbl0561.57001
  17. [17] H. Seifert, Topologie dreidimensionaler gefaserter Räume, Acta Math. 60 (1932), 147-238. Zbl0006.08304
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  19. [19] A. R. Shastri, J. G. Williams and P. Zvengrowski, Kinks in general relativity, International Journal of Theoretical Physics 19 (1980), 1-23. Zbl0448.55009
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