The depth and LS category of a topological space

• Yves Félix ^[1] ; Steve Halperin ^[2]
  1. [1] Université Catholique de Louvain

     Université Catholique de Louvain

     Arrondissement de Nivelles, Bélgica

     
  2. [2] University of Maryland (Estados Unidos)
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 123, Nº 2, 2018, págs. 220-238
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The depth of an augmented ring ε:A→k is the least p, or ∞, such that \begin {equation*} \Ext _A^p(k , A)\neq 0. \end {equation*} When X is a simply connected finite type CW complex, H∗(ΩX;Q) is a Hopf algebra and the universal enveloping algebra of the Lie algebra LX of primitive elements. It is known that \depthH∗(ΩX;Q)≤\catX, the Lusternik-Schnirelmann category of X.

    For any connected CW complex we construct a completion Hˆ(ΩX) of H∗(ΩX;Q) as a complete Hopf algebra with primitive sub Lie algebra LX, and define \depthX to be the least p or ∞ such that \ExtpULX(Q,Hˆ(ΩX))≠0.

    Theorem: for any connected CW complex, \depthX≤\catX.