[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180326

A PROSET STRUCTURE INDUCED FROM HOMOTOPY CLASSES OF MAPS AND A CLASSIFICATION OF FIBRATIONS

Yamaguchi, Toshihiro (Faculty of Education Kochi University)
Yokura, Shoji (Department of Mathematics and Computer Science Graduate School of Science and Engineering Kagoshima University)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.3, 2019 , pp. 991-1004 More about this Journal

Abstract

Firstly we consider preorders (not necessarily partial orders) on a canonical quotient of the set of the homotopy classes of continuous maps between two spaces induced by a certain equivalence relation ${\sim}_{{\varepsilon}R}$ . Secondly we apply it to a classification of orientable fibrations over Y with fibre X. In the classification theorem of J. Stasheff [22] and G. Allaud [3], they use the set $$[Y,\;Baut_1X$ $]$ $$$ of homotopy classes of continuous maps from Y to $Baut_1X$ , which is the classifying space for fibrations with fibre X due to A. Dold and R. Lashof [11]. In this paper we give a classification of fibrations using a preordered set (abbr., proset) structure induced by $$[Y,\;Baut_1X$ $]$ $_{{\varepsilon}R}:=[Y,\;Baut_1X$ $]$ $/{\sim}_{{\varepsilon}R}$$ .

Keywords

homotopy set; proset; orientable fibration; classifying space; rational homotopy; Sullivan minimal model;

Citations & Related Records

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