We present an explanation for the well-known observation that complexity of the solar magnetic field is a necessary ingredient for strong activity such as large eruptive flares. Our model starts with the standard picture for the energy build up -- highly-sheared, newly-emerged magnetic field near the photospheric neutral line held down by overlying unsheared field. Previously, we proposed the key new idea that magnetic reconnection between the unsheared field and neighboring flux systems decreases the amount of overlying field and, thereby, allows the low-lying sheared flux to ``break out (Antiochos, DeVore and Klimchuk 1998, ApJ, submitted). In this paper we show that a bipolar active region does not have the necessary complexity for this process to occur, but a delta sunspot has the right topology for magnetic breakout. We discuss the implications of these results for observations from SOHO and TRACE.
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