A minimum dimensional counterexample to Ganea's conjecture

Donald Stanley,Hugo Rodríguez Ordóñez

doi:10.1016/j.topol.2010.06.009

A minimum dimensional counterexample to Ganea's conjecture

Donald Stanley, Hugo Rodríguez Ordóñez

Open Access

https://doi.org/10.1016/j.topol.2010.06.009

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Journal: Topology and its Applications	Publication Date: Jul 5, 2010
Citations: 3	License type: publisher-specific-oa

Affiliation: University of Regina, Autonomous University of Aguascalientes

#Ganea's Conjecture #Lusternik Schnirelmann Category + Show 5 more

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Abstract

A 7-dimensional CW-complex having Lusternik–Schnirelmann category equal to 2 is constructed. Using a divisibility phenomenon for Hopf invariants, it is proved that the Cartesian product of the constructed complex with a sphere of sufficiently large dimension also has category 2. This space hence constitutes the minimum dimensional known counterexample to Ganea's conjecture on the Lusternik–Schnirelmann category of spaces.

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