I am reading the paper "http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.61.1029" by Haldane where he calculates the Berry phase associated with instanton or hedgehog events in the O(3) nonlinear sigma model (described by the unit vectors Ω(*x*,*y*,*t*)). On page 2 last paragraph he says that a hedgehog event will create ±4*π* vortex of* w*(*x*,*y*) at the spatial center of the hedghog, where *w*(*x*,*y*) is supposed to be the Berry phase obtained by the closed loop defined by the time evolution of eΩ(*x*,*y*,*t*). I am confused by this statement, because after the hedgehog event, the initial field configuration has changed to a configuration with a different skyrmion number and Ω(*x*,*y*,*t*) does not define a closed loop. So, I don't understand what he means by *w*(*x*,*y*) in this case. If somebody can clarify this, it will be very helpful.