Open Access
november 2013 When does secat equal relcat ?
Jean-Paul Doeraene, Mohammed El Haouari
Bull. Belg. Math. Soc. Simon Stevin 20(5): 769-776 (november 2013). DOI: 10.36045/bbms/1385390762


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.


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Jean-Paul Doeraene. Mohammed El Haouari. "When does secat equal relcat ?." Bull. Belg. Math. Soc. Simon Stevin 20 (5) 769 - 776, november 2013.


Published: november 2013
First available in Project Euclid: 25 November 2013

zbMATH: 1288.55001
MathSciNet: MR3160587
Digital Object Identifier: 10.36045/bbms/1385390762

Primary: 55M30

Keywords: Ganea fibration , sectional category , topological complexity

Rights: Copyright © 2013 The Belgian Mathematical Society

Vol.20 • No. 5 • november 2013
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