The depth and LS category of a topological space

Authors

  • Yves Félix
  • Steve Halperin

DOI:

https://doi.org/10.7146/math.scand.a-106920

Abstract

The depth of an augmented ring ε:Ak 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 ˆH(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,ˆH(ΩX))0. Theorem: for any connected CW complex, \depthX\catX.

References

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Published

2018-09-05

How to Cite

Félix, Y., & Halperin, S. (2018). The depth and LS category of a topological space. MATHEMATICA SCANDINAVICA, 123(2), 220–238. https://doi.org/10.7146/math.scand.a-106920

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