Just before he died, Ganea attended the Symposium on Algebraic Topology, held February 22–26, 1971 at the Battelle Seattle Research Center, in Seattle. At the symposium, he was not able to give a talk, but he did distribute a preprint containing a list of unsolved problems. One of these problems, regarding the "Lusternik–Schnirelmann category", came to be known as "Ganea's conjecture". A version of this conjecture for rational spaces was proved by Kathryn Hess in her 1989 MIT Ph.D. thesis. Many particular cases of Ganea's original conjecture were proved, until Norio Iwase provided a counterexample in 1998.