3 papers
math.AT2023
A study of the Ganea conjecture for topological complexity by using weak topological complexity
Jose M. Garcia-Calcines, Lucile Vandembroucq
In this paper, we provide sufficient conditions for a space to satisfy the Ganea conjecture for topological complexity. To achieve this, we employ two auxiliary invariants: wea…
math.AT2014
Brown representability for exterior cohomology and cohomology with compact supports
J. M. García-Calcines, P. R. García-Díaz, A. Murillo
It is well known that cohomology with compact supports is not a homotopy invariant but only a proper homotopy one. However, as the proper category lacks of general categorical prop…
math.DS2012
A completion construction for continuous dynamical systems
J. M. Garcia Calcines, L. J. Hernandez Paricio, M. T. Rivas Rodriguez
In this work we construct the $\Co^{\r}$-completion and $\Co^ł$-completion of a dynamical system. If is a flow, we construct canonical maps $X\to \Co^{\r}(X)$ and $X\to \Co^ł(X…