The Category of a Map and the Grade of a Module

Félix, Yves;Halperin, S.;Thomas, JC.
(1992) Israel Journal of Mathematics — Vol. 78, n° 2-3, p. 177-196 (1992)

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Authors
  • Félix, YvesUCLouvain
    Author
  • Halperin, S.
    Author
  • Thomas, JC.
    Author
Abstract
Let f : Y --> X be a continuous map between connected CW complexes. The homology H* (F) of the homotopy fibre is then a module over the loop space homology H* (OMEGAX). THEOREM: If H*(F; R) and H*(OMEGAX; R) are R-free (R a principal ideal domain) then for some H*(OMEGAX; R)-projective module P=P(greater-than-or-equal-to 0) and for some m less-than-or-equal-to cat f: Ext(H* (OMEGAX)m(H* (F); P) not-equal 0. Some applications are also given.
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Félix, Y., Halperin, S., & Thomas, JC. (1992). The Category of a Map and the Grade of a Module. Israel Journal of Mathematics, 78(2-3), 177-196. https://doi.org/10.1007/BF02808056 (Original work published 1992)