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A topological proof of Wolpert's formula for the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates
We introduce a natural cell decomposition of a closed oriented surface associated with a pants decomposition, and an explicit groupoid cocycle on the cell decomposition which represents each point of the Teichm\"uller space $\mathcal{T}_g$. We call it the {\it standard cocycle} of the point of $\mathcal{T}_g$. As an application of …