Bulletin of the Belgian Mathematical Society - Simon Stevin

When does secat equal relcat ?

Jean-Paul Doeraene and Mohammed El Haouari

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Abstract

In [3] the authors introduced a {\em relative category} for a map that differ from the {\em sectional category} by just one. The relative category has specific properties (for instance a homotopy pushout does not increase it) which make it a convenient tool to study the sectional category. The question to know when secat equals relcat arises. We give here some sufficient conditions. Applications are given to the {\em topological complexity}, which is nothing but the sectional category of the diagonal.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 5 (2013), 769-776.

Dates
First available in Project Euclid: 25 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1385390762

Digital Object Identifier
doi:10.36045/bbms/1385390762

Mathematical Reviews number (MathSciNet)
MR3160587

Zentralblatt MATH identifier
1288.55001

Subjects
Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space

Keywords
Ganea fibration sectional category topological complexity

Citation

Doeraene, Jean-Paul; El Haouari, Mohammed. When does secat equal relcat ?. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 5, 769--776. doi:10.36045/bbms/1385390762. https://projecteuclid.org/euclid.bbms/1385390762


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