%0 Generic %1 Sibilla2011 %A Sibilla, Nicoló %A Treumann, David %A Zaslow, Eric %D 2011 %K graphs mirror ribbon symmetry %T Ribbon Graphs and Mirror Symmetry I %U http://arxiv.org/abs/1103.2462 %X Given a ribbon graph $\Gamma$ with some extra structure, we define, using constructible sheaves, a dg category $CPM(\Gamma)$ meant to model the Fukaya category of a Riemann surface in the cell of Teichm"uller space described by $\Gamma.$ When $\Gamma$ is appropriately decorated and admits a combinatorial "torus fibration with section," we construct from $\Gamma$ a one-dimensional algebraic stack $X_\Gamma$ with toric components. We prove that our model is equivalent to $Perf(X_\Gamma)$, the dg category of perfect complexes on $X_\Gamma$.

@misc{Sibilla2011, abstract = { Given a ribbon graph $\Gamma$ with some extra structure, we define, using constructible sheaves, a dg category $CPM(\Gamma)$ meant to model the Fukaya category of a Riemann surface in the cell of Teichm\"uller space described by $\Gamma.$ When $\Gamma$ is appropriately decorated and admits a combinatorial "torus fibration with section," we construct from $\Gamma$ a one-dimensional algebraic stack $\widetilde{X}_\Gamma$ with toric components. We prove that our model is equivalent to $Perf(\widetilde{X}_\Gamma)$, the dg category of perfect complexes on $\widetilde{X}_\Gamma$. }, added-at = {2011-03-15T13:11:14.000+0100}, author = {Sibilla, Nicoló and Treumann, David and Zaslow, Eric}, biburl = {https://www.bibsonomy.org/bibtex/234d948b06fec300d3a6e1cd4ad5e2b2f/uludag}, description = {[1103.2462] Ribbon Graphs and Mirror Symmetry I}, interhash = {73c27404c9639bd7bd656ab409ee7376}, intrahash = {34d948b06fec300d3a6e1cd4ad5e2b2f}, keywords = {graphs mirror ribbon symmetry}, note = {cite arxiv:1103.2462 Comment: 28 pages}, timestamp = {2011-03-15T13:41:27.000+0100}, title = {Ribbon Graphs and Mirror Symmetry I}, url = {http://arxiv.org/abs/1103.2462}, year = 2011 }