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Publication . Preprint . Article . 2015 . Embargo end date: 01 Jan 2015

Yet another Hopf Invariant

Doeraene, Jean-Paul; Haouari, Mohammed El;
Open Access
Published: 15 Jan 2015
Publisher: arXiv

The classical Hopf invariant is defined for a map f: S^r -> X. Here we define `hcat' which is some kind of Hopf invariant built with a construction in Ganea's style, valid for maps not only on spheres but more generally on a `relative suspension' f: Sigma_A W -> X. We study the relation between this invariant and the sectional category and the relative category of a map. In particular, for f being the `restriction' of f on A, we have relcat(i) <= hcat(f) <= relcat(i) + 1 and relcat(f) <= hcat(f).


Algebraic Topology (math.AT), FOS: Mathematics, 55Q25, 55M30, Mathematics - Algebraic Topology

// S [1] Jean-Paul Doeraene. About sectional category of the ganea maps, 2015. arXiv:1507.07752. [OpenAIRE]

[2] Jean-Paul Doeraene and Mohammed El Haouari. Up-to-one approximations for sectional category and topological complexity. Topology and its Appl., 160:766-783, 2013.

[3] Norio Iwase. Ganea's conjecture on lusternik-schnirelmann category. Bull. Lond. Math. Soc., 30:623-634, 1198.

[4] Michael Mather. Pull-backs in homotopy theory. Canad. Journ. Math., 28(2):225-263, 1976.

[5] George W. Whitehead. Elements of homotopy theory, volume 64 of Graduate texts in mathematics. Springer-Verlag, New York, 1978.