Lucile Vandembroucq (8/25/22): On the weak topological complexity and the TC-Ganea conjecture
By analogy with the classical Ganea conjecture, which has been disproved by N. Iwase, the TC-Ganea conjecture asks whether the equality TC(X x S^n)=TC(X)+TC(S^n) holds for all finite CW complexes X and all positive integers n. In a previous work in collaboration with J. González and M. Grant, we have constructed a space X satisfying TC(X x S^n)=TC(X)+1 for all n greater than 1, which proves that the TC-conjecture fails for even n. In this talk, we will use the notion of weak topological complexity to establish some sufficient conditions for a space X to satisfy TC(X x S^n)=TC(X)+TC(S^n). This is a joint work with J. Calcines.