Given a smooth oriented closed surface of genus zero, possible with boundary, we first fixed a G-cover of this surface where G is a fixed finite group. To understand this, we break down this G cover into several pieces and each piece is identified with a G cover of sphere with certain number of holes. We called G cover of sphere with holes a “standard blocks”. Given a G cover of a surface, there are many different ways to identify this G cover with gluing of one or several “standard blocks”. We give a description of all the ways in which a given G cover can be obtain by such a gluing process. In the case when G is a trivial group, this kind of gluing process is called “Lego-Teichmuller game”. We extend t his notion of “Lego-Teichmuller game” in more general situation when G is a finite group. First, we consider a complex where each vertex is such an identification. Then we define some simple moves and relations which will turn this complex into a connected and simply connected complex. This will be used in the future paper to construct Gequivariant modular functor. This G-equivariant modular functor will be an extension of the usual modular functor.
|School:||State University of New York at Stony Brook|
|School Location:||United States -- New York|
|Source:||DAI-B 69/12, Dissertation Abstracts International|
|Subjects:||Mathematics, Theoretical physics|
|Keywords:||G-cover, Lego-Teichmuller game, Modular functor, Topology|
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