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Connective K ‐Theoretic Euler Classes and Non‐Immersions of 2 k ‐Lens Spaces
Author(s) -
González Jesús
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001769
Subject(s) - euler's formula , lens (geology) , mathematics , pure mathematics , mathematical analysis , physics , optics
The paper studies the connective complex K ‐theoretic Euler class of a certain bundle associated to a Euclidean immersion of the lens space L (2 k ) 2 n +1 to show that this manifold cannot be immersed in R 4 n −2α( n ) if k ⩾ α( n ). The non‐immersion is best possible in many cases. This suggests a close relationship between the immersion problem for complex projective spaces and that for ‘high’ 2‐torsion lens spaces.