Explore a 57-minute lecture on the nonmaximality of topological complexity for manifolds with abelian fundamental groups. Delve into sufficient conditions for closed manifolds M with abelian fundamental groups to have nonmaximal normalized topological complexity, where TC(M) is less than 2dim(M). Examine examples demonstrating the sharpness of these conditions, generalizing Costa and Farber's results on spaces with small fundamental groups. Investigate the extension of Dranishnikov's findings on LS-category for nonorientable surfaces to a broader class of manifolds by relaxing the commutativity condition of the fundamental group. Gain insights into joint work with Dan Cohen on the nonmaximality of the LS-category for the cofibre of the diagonal map Δ: M → M × M in various manifolds.