It is noted that Hartly-Hawking's wave function of the ground state of the universe is equal to zero when its arguments (i.e. the universe and matter fields in it) satisfy some topological conditions. These conditions are obtained in explicit form in particular cases. The possible consequence is the statement that the baryon charge of our universe would be zero in the absence of baryon-number violating interactions.I am indebted to H.M. Asatryan, V.G. Gurzadyan, S.G. Matinyan and O.M. Khudaverdyan for the interest in this work and discussions; to A.D. Linde, V.A. Rubakov, B.L. Spokoiny and A.A. Starobinsky for discussions on the problem of the quantum birth of the universe; and also to A.O. Barvinsky, V.A. Kazakov, A.A. Migdal and A.S. Schwarz for discussions on different aspects of the present work.