On the Weak Topological Complexity and the TC-Ganea Conjecture

Explore the intricacies of the TC-Ganea conjecture in this 50-minute conference talk delivered by Lucile Vandembroucq for the Applied Algebraic Topology Network. Delve into the analogy with the classical Ganea conjecture and its disproval by N. Iwase. Examine the speaker's previous collaborative work with J. González and M. Grant, which constructed a space X satisfying TC(X x S^n)=TC(X)+1 for all n greater than 1, disproving the TC-conjecture for even n. Learn about the concept of weak topological complexity and discover sufficient conditions for a space X to satisfy TC(X x S^n)=TC(X)+TC(S^n), based on joint research with J. Calcines. Gain insights into advanced topics in algebraic topology and expand your understanding of topological complexity.