Membrane Interactions
One of the reasons M-theory is so difficult to formulate is that the numbers of different types of membranes in the various dimensions increases exponentially. For example once one gets to 3-dimensional surfaces, one has to deal with solid objects with knot-shaped holes, and then one needs the whole of knot theory just to classify them. Since M-theory is thought to operate in 11 dimensions this problem then becomes very difficult. But just like string theory, in order for the theory to satisfy causality, the theory must be local, and so the topology changing must occur at a single point. The basic orientable 2-brane interactions are easy to show. Orientable 2-branes are tori with multiple holes cut out of them.
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