Postnikov factorizations at infinity

Aldana, José Ignacio Extremiana; Paricio, Luis Javier Hernández; Rodríguez, María Teresa Rivas

doi:10.1016/j.topol.2003.07.022

Cited by 8 publications

(11 citation statements)

References 16 publications

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“…The new category of exterior spaces and maps is complete and cocomplete and contains as a full subcategory the category of spaces and proper maps, see [9,10]. For more properties and applications of exterior homotopy categories we refer the reader to [7,12] and for a survey of proper homotopy to [20].…”

Section: The Category Of Proper and Exterior Spacesmentioning

confidence: 99%

“…If instead of n-spheres we use sequences of n-spheres converging to infinity, then we obtain the Brown-Grossman proper homotopy groups π N q , see [1,15]. On the other hand, if we move an n-sphere continuously towards infinity, we get infinite semitubes which represent elements of the Steenrod proper homotopy groups, see [5,7,8]. The analog of the previous groups have been considered for the category of exterior spaces, see [9,10].…”

Section: Introductionmentioning

confidence: 99%

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S-types of Global Towers of Spaces and Exterior Spaces

Río

Hernández

Rivas

2008

Appl Categor Struct

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The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact spaces and manifolds. The notion of exterior weak N-S-equivalences is given by exterior maps which induce isomorphisms on the k-th N-exterior homotopy groups π N k for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray localized by exterior weak N-S-equivalences is called the category of exterior N-Stypes. The existence of closed model structures in the category of exterior spaces permits to establish equivalences between homotopy categories obtained by dividing by exterior homotopy relations, and categories of fractions (localized categories) given by the inversion of classes of week equivalences. The family of neighbourhoods 'at infinity' of an exterior space can be interpreted as a global prospace and under the condition of first countable at infinity we can consider a global tower instead of a prospace. The objective of this paper is to use localized categories to find the connection between S-types of exterior spaces and S-types of global towers of spaces. The main result of this paper establishes an equivalence between the category of Stypes of rayed first countable exterior spaces and the category of S-types of global towers of pointed spaces. As a consequence of this result, categories of global towers of algebraic models localized up to weak equivalences can be used to give some algebraic models of S-types.The authors acknowledge the financial support given by the projects FOMENTA 2007/03 and MTM2007-65431.

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Section: The Category Of Proper and Exterior Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

S-types of Global Towers of Spaces and Exterior Spaces

Río

Hernández

Rivas

2008

Appl Categor Struct

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“…The category of exterior spaces has been provided with a well developed homotopy theory ( [12,[16][17][18]21]). The study of the exterior and proper homotopy invariants has proved to be useful in the study of non-compact manifolds ( [8,30]), the study of the shape of some compact spaces ( [22]), the L-S proper category ( [14,15]), et cetera.…”

Section: Introductionmentioning

confidence: 99%

“…The new category of exterior spaces and maps is complete and cocomplete and contains as a full subcategory the category of spaces and proper maps, see [16,17]. We refer to [9,11,12,21,22] for further properties and applications of exterior homotopy, and to [26] for a survey of proper homotopy.…”

mentioning

confidence: 99%

Omega limits, prolongational limits and almost periodic points of a continuous flow via exterior spaces

Calcines

Paricio

Rodríguez

2017

Glas. Mat. Ser. III

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Abstract. In this paper we analyse some applications of the category of exterior spaces to the study of dynamical systems (flows). The limit space and end space of an exterior space are used to construct different types of limit spaces and end spaces of a dynamical system. In this work we analyse the relationships between the notions and constructions given by the exterior structures of a continuous flow and the more usual notions of omega-limits, first prolongational limits and several types of almost periodic points (Poisson-stable points, non-wandering points) of a flow.

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“…We shall also strongly need the use of exterior Postnikov factorizations developed in [14]: Given an exterior space X , there is an exterior homotopy commutative diagram:…”

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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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Postnikov factorizations at infinity

Cited by 8 publications

References 16 publications

S-types of Global Towers of Spaces and Exterior Spaces

S-types of Global Towers of Spaces and Exterior Spaces

Omega limits, prolongational limits and almost periodic points of a continuous flow via exterior spaces

The Ganea conjecture in proper homotopy via exterior homotopy theory

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