A Whitehead–Ganea approach for proper Lusternik–Schnirelmann category

Calcines, José Manuel García; García-Díaz, P. R.; Murillo-Mas, Aniceto

doi:10.1017/s0305004106009960

Cited by 9 publications

(11 citation statements)

References 23 publications

(37 reference statements)

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“…After reindexing, if necessary, we can assume α([i, ∞)) ⊂ X i . In [18] it is proved that there exists a sequence of well-defined Ganea fibrations in E *…”

Section: Proper Ls Categorymentioning

confidence: 99%

Detecting cohomology classes for the proper LS category. The case of semistable 3-manifolds

Cárdenas

Lasheras

Quintero

2011

Math. Proc. Camb. Phil. Soc.

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Link to this article: http://journals.cambridge.org/abstract_S0305004111000417 How to cite this article: MANUEL CÁRDENAS, FRANCISCO F. LASHERAS and ANTONIO QUINTERO (2012). Detecting cohomology classes for the proper LS category. The case of semistable 3-manifolds. Mathematical AbstractWe give sufficient conditions for the existence of detecting elements for the LusternikSchnirelmann category in proper homotopy. As an application we determine the proper LS category of some semistable one-ended open 3-manifolds.

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“…After reindexing, if necessary, we can assume α([i, ∞)) ⊂ X i . In [18] it is proved that there exists a sequence of well-defined Ganea fibrations in E *…”

Section: Proper Ls Categorymentioning

confidence: 99%

Detecting cohomology classes for the proper LS category. The case of semistable 3-manifolds

Cárdenas

Lasheras

Quintero

2011

Math. Proc. Camb. Phil. Soc.

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“…We first recall basic facts on LS invariants in the exterior setting from the axiomatic point of view and its consequences in the study of proper LS-category [17]. Henceforth, the normalized version (category zero for "contractible" spaces) of exterior and proper LS invariants shall be used.…”

Section: Ganea Conjecture On Proper Ls-categorymentioning

confidence: 99%

“…Recall that the category of exterior spaces [18,19] (see also next section for definitions and basic facts) is complete, cocomplete, it contains the proper category through a full embedding, and it is a J -category [17] in the sense of Doeraene [12]. Recall that the category of exterior spaces [18,19] (see also next section for definitions and basic facts) is complete, cocomplete, it contains the proper category through a full embedding, and it is a J -category [17] in the sense of Doeraene [12].…”

Section: Introductionmentioning

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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“…To see recient applications of the category of exterior spaces to proper homotopy theory we refer the reader to [19].…”

Section: 4mentioning

confidence: 99%

Exact Sequences and Closed Model Categories

Pinillos

Paricio

Rodríguez

2009

Appl Categor Struct

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Abstract. For every closed model category with zero object, Quillen gave the construction of Eckman-Hilton and Puppe sequences.In this paper, we remove the hypothesis of the existence of zero object and construct (using the category over the initial object or the category under the final object) these sequences for unpointed model categories.We illustrate the power of this result in abstract homotopy theory given some interesting applications to group cohomology and exterior homotopy groups.

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A Whitehead–Ganea approach for proper Lusternik–Schnirelmann category

Cited by 9 publications

References 23 publications

Detecting cohomology classes for the proper LS category. The case of semistable 3-manifolds

Detecting cohomology classes for the proper LS category. The case of semistable 3-manifolds

The Ganea conjecture in proper homotopy via exterior homotopy theory

Exact Sequences and Closed Model Categories

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