Bounds for the cup-length of Poincaré spaces and their applications |
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| Authors: | Jú lius Korba&scaron |
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| Affiliation: | a Department of Algebra, Geometry, and Mathematical Education, Faculty of Mathematics, Physics, and Informatics, Comenius University, Mlynská dolina, SK-842 48 Bratislava 4, Slovakia
b Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava 1, Slovakia |
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| Abstract: | Our main result offers a new (quite systematic) way of deriving bounds for the cup-length of Poincaré spaces over fields; we outline a general research program based on this result. For the oriented Grassmann manifolds, already a limited realization of the program leads, in many cases, to the exact values of the cup-length and to interesting information on the Lyusternik-Shnirel'man category. |
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| Keywords: | primary, 57N65, 55M30 secondary, 53C30 |
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