Abstract:
A thickening of a finite CW-complex X is by definition a compact manifold M of the same simple homotopy type as X. We give a model for the cochain complex of the boundary of that manifold, C *(δM), as a module over the cochain algebra C *(X). We also show how to construct an algebraic model of the rational homotopy type of δC *(M) from a model of X. Using this rational model, we prove a new formula for the rational Lusternik–Schnirelmann category of X.
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Received: 24 September 1999
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Lambrechts, P. Cochain model for thickenings and its application to rational LS-category. manuscripta math. 103, 143–160 (2000). https://doi.org/10.1007/s002290070017
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DOI: https://doi.org/10.1007/s002290070017