Suspension of Ganea fibrations and a Hopf invariant

Vandembroucq, Lucile

doi:10.1016/s0166-8641(99)00058-9

Cited by 13 publications

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“…To prove the result above we shall use the approach in [26] overcoming the obstacles created by the lack of good homology properties in exterior homotopy theory. To prove the result above we shall use the approach in [26] overcoming the obstacles created by the lack of good homology properties in exterior homotopy theory.…”

Section: Ganea Conjecture On Proper Ls-categorymentioning

confidence: 99%

The Ganea conjecture in proper homotopy via exterior homotopy theory

Calcines

Díaz

Murillo-Mas

2010

Math. Proc. Camb. Phil. Soc.

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Link to this article: http://journals.cambridge.org/abstract_S0305004110000174 How to cite this article: JOSE M. GARCÍA-CALCINES, PEDRO R. GARCÍA-DÍAZ and ANICETO MURILLO MAS (2010). The Ganea conjecture in proper homotopy via exterior homotopy theory. Mathematical AbstractIn this article we provide sufficient conditions on a space X to verify Ganea conjecture with respect to exterior and proper Lusternik-Schnirelmann category. For this aim we previously develop an exterior version of the Whitehead, cellular approximation, CWapproximation and Blakers-Massey theorems within a homotopy theory of exterior CWcomplexes and study their corresponding analogues and consequences in the proper setting.

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Section: Ganea Conjecture On Proper Ls-categorymentioning

confidence: 99%

The Ganea conjecture in proper homotopy via exterior homotopy theory

Calcines

Díaz

Murillo-Mas

2010

Math. Proc. Camb. Phil. Soc.

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“…For example, the σ i cat (X) (see [32]) is the smallest n such that the i-fold suspension of the n-th Ganea fibration admits a section:…”

Section: Fiberwise Functorial Extensionmentioning

confidence: 99%

“…These are invariants associated by the above process to the fiberwise extension of the functors p p and ∞ ∞ . We will also use the invariant associated to the functor ∞ called σ category as in [32], which also coincides with the invariant r(M) of [24].…”

Section: Introductionmentioning

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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“…In fact, Iwase [32] was the first to produce a whole family of counterexamples, the lowest dimensional of which has dimension 10. According to [47], Vandembroucq [52] proves that no counterexamples to Ganea's conjecture can exist in dimension at most five. Also, for simply connected spaces of dimension 6 no such counterexamples can exist [48].…”

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confidence: 99%

Old and new categorical invariants of manifolds

Gómez-Larrañaga

González-Acuña

Heil³

2014

Bol. Soc. Mat. Mex.

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The Lusternik-Schnirelmann category of a space X is the smallest number of open and (in X ) contractible sets that cover X . More generally, a categorical invariant of X is defined to be the smallest number of open sets that cover X and that have certain properties. For example, the sets may be required to be contractible in themselves; or the inclusion of each of the sets may be required to factor homotopically through some fixed given space K ; or for each component of the sets the inclusion into X may be required to be π 1 -injective; or for each component of the sets the image of the fundamental group under the homomorphism induced by inclusion into X may be required to belong to a given class of groups (e.g. the class of amenable or the class of solvable groups). The aim of this paper is to describe several such categorical Dedicated to Fico González-Acuña on his 70th birthday.

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Suspension of Ganea fibrations and a Hopf invariant

Cited by 13 publications

References 0 publications

The Ganea conjecture in proper homotopy via exterior homotopy theory

The Ganea conjecture in proper homotopy via exterior homotopy theory

Lagrangian intersections, critical points and Qcategory

Old and new categorical invariants of manifolds

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