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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