Fibrewise suspension and Lusternik–Schnirelmann category

Vandembroucq, Lucile

doi:10.1016/s0040-9383(02)00007-1

Cited by 11 publications

(18 citation statements)

References 11 publications

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“…This invariant was introduced by F. Laudenbach and J.-C. Sikhorav in [12]. Our proof shows that the category of the space Sp(3) coincides with the cone length of Sp(3) and with a stabilized version of the category, denoted Qcat(Sp(3)); see [17,25]. From the main theorem of P.-M. Moyaux and L. Vandembroucq in [15] we know that Crit(Sp(3)) − 1 is less than the cone length and is bounded below by Qcat.…”

Section: Introductionmentioning

confidence: 72%

The Lusternik-Schnirelmann category of 𝑆𝑝(3)

Suárez

Gómez-Tato

Strom

et al. 2003

Proc. Amer. Math. Soc.

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Section: Introductionmentioning

confidence: 72%

The Lusternik-Schnirelmann category of 𝑆𝑝(3)

Suárez

Gómez-Tato

Strom

et al. 2003

Proc. Amer. Math. Soc.

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“…We set (see [33]) Our aim is now to prove Proposition 5. For any space X of the homotopy type of a CW -complex,…”

Section: T T T T T T T T Q K+1 (Z)mentioning

confidence: 99%

“…Thus, by unicity of the fiberwise extension ( [33], Prop. 2), R p+1 X (G n+1 (X, p)) → X is the fiberwise extension of R p+1 applied to g n .…”

Section: T T T T T T T T Q K+1 (Z)mentioning

confidence: 99%

Lagrangian intersections, critical points and Qcategory

Moyaux

Vandembroucq

2004

Mathematische Zeitschrift

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For a manifold M, we prove that any function defined on a vector bundle of basis M and quadratic at infinity has at least Qcat (M) + 1 critical points. Here Qcat (M) is a homotopically stable version of the LS-category defined by Scheerer, Stanley and Tanré [27]. The key homotopical result is that Qcat (M) can be identified with the relative LS-category of Fadell and Husseini [9] of the pair (M × D n+1 , M × S n ) for n big enough. Combining this result with the work of Laudenbach and Sikorav [19], we obtain that if M is closed, for any hamiltonian diffeomorphism with compact support ψ of T * M, #(ψ(M) ∩ M) ≥ Qcat (M) + 1, which improves all previously known homotopical estimates of this intersection number. (2000): 53D12, 55M30, 57R70. Mathematics Subject Classification

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“…If p is a fibration of fibre F , then Σ B E → B is a fibration of the fibre ΣF and Σ B E + → B a fibration of the fibre ΣF + (cf. [18,Lemma 6]).…”

Section: Introductionmentioning

confidence: 99%

Fibrewise stable rational homotopy

Félix

Murillo

Tanré

2010

Journal of Topology

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In this paper, for a given space B, we establish a correspondence between differential graded modules over C*(B; ℚ) and fibrewise rational stable spaces over B. This correspondence opens the door for topological translations of algebraic constructions made with modules over a commutative differential graded algebra. More precisely, given the fibrations E→B and E′→B, the set of stable rational homotopy classes of maps over B is isomorphic to Ext*C*(B;ℚ) (C*(E′; ℚ), C*(E; ℚ)). In particular, a nilpotent finite‐type CW‐complex X is a rational Poincaré complex if there exist non‐trivial stable maps over Xℚ from (X × Sq)ℚ to (X ∨ Sq+N)ℚ for exactly one N.

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Fibrewise suspension and Lusternik–Schnirelmann category

Cited by 11 publications

References 11 publications

The Lusternik-Schnirelmann category of 𝑆𝑝(3)

The Lusternik-Schnirelmann category of 𝑆𝑝(3)

Lagrangian intersections, critical points and Qcategory

Fibrewise stable rational homotopy

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