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arXiv · 1403.8089

Relative category and monoidal topological complexity

J. G. Carrasquel-Vera·J. M. García Calcines·L. Vandembroucq
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Abstract

If a map $f$ has a homotopy retraction, then Doeraene and El Haouari conjectured that the sectional category and the relative category of $f$ are the same. In this work we discuss this conjecture for some lower bounds of these invariants. In particular, when we consider the diagonal map, we obtain results supporting Iwase-Sakai's conjecture which asserts that the topological complexity is the monoidal topological complexity.

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J. G. Carrasquel-Vera, J. M. García Calcines, L. Vandembroucq. 2014-03-31. Relative category and monoidal topological complexity. https://arxiv.org/abs/1403.8089

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