Mathematics Colloquia and Seminars

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We consider a special class of Riemann surfaces whose transition maps lie in PSL(2,C). This structure is called a complex projective structure. There is an operation on a complex projective structure called grafting. Roughly speaking a grafting gives an extra covering on the Riemann sphere to the “global” coordinate of the complex projective structure. This operation is done along a “good” loop on the surface. For certain types of complex projective structures, in particular when the holonomy representation is Fuchsian, a sequence of grafting operations can be composed in a combinatorial way about the loops we graft along. The talk will contain some simple examples to illustrate the key idea, as well as a number of pictures.