The rational ls category of products and of Poincaré duality complexes

Félix, Yves; Halperin, Stephen; Lemaire, Jean-Michel

doi:10.1016/s0040-9383(97)00061-x

Cited by 32 publications

(24 citation statements)

References 8 publications

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“…So the ΛX-module morphism from ΛX to P * which sends 1 to z + ∂α is a weak equivalence and factors over (P * /I n+1 ). By [FHL,Prop. 2iii)], it follows that M -cat(ΛX) n. Now suppose that M -cat(ΛX) n. By [FHL,Prop.…”

Section: Proof Suppose E((λx)mentioning

confidence: 99%

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Lusternik-Schnirelmann category and products of local spaces

Stelzer

2009

Homology, Homotopy and Applications

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Section: Proof Suppose E((λx)mentioning

confidence: 99%

“…By [FHL,Prop. 2iii)], it follows that M -cat(ΛX) n. Now suppose that M -cat(ΛX) n. By [FHL,Prop. 3], one knows that M -cat(N ) M -cat(ΛX) for every N ∈ ΛX − mod.…”

Section: Proof Suppose E((λx)mentioning

confidence: 99%

Lusternik-Schnirelmann category and products of local spaces

Stelzer

2009

Homology, Homotopy and Applications

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“…This likewise corresponds to a map f 2 : Y 2 → X injective in rational homotopy. Note that Y 2 fibres rationally over S 3 with fibre X [9] , the 9-connective cover of X. The images (f j ) # π * (Y jQ ) in π * (X Q ) are distinct.…”

Section: (E)] For Details)mentioning

confidence: 99%

A mapping theorem for topological complexity

Grant

Lupton

Oprea

2015

Algebr. Geom. Topol.

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Abstract. We give new lower bounds for the (higher) topological complexity of a space, in terms of the Lusternik-Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and more generally for the rational sectional category of a map, in terms of the rational category of a certain auxiliary space. We use our results to deduce consequences for the global (rational) homotopy structure of simply connected, hyperbolic finite complexes.

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“…This conjecture was proved to be false in the general case by Iwase [12] but it remains true in the rational category. For example, see Félix, Halperin and Lemaire [6], Hess [11] and Jessup [13]. Here, a final application to the Ganea conjecture for rational topological complexity is obtained using mtc.…”

Section: Definition 12 Consider the Projectionmentioning

confidence: 99%