An $A_∞$-structure for lines in a plane TeX Export

@misc{citeulike:2277303, abstract = {As an explicit example of an \$A\_\infty\$-structure associated to geometry, we construct an \$A\_\infty\$-structure for a Fukaya category of finitely many lines (Lagrangians) in \$\R^2\$, ie., we define also {\em non-transversal} \$A\_\infty\$-products. This construction is motivated by homological mirror symmetry of (two-)tori, where \$\R^2\$ is the covering space of a two-torus. The strategy is based on an algebraic reformulation of Morse homotopy theory through homological perturbation theory (HPT) as discussed by Kontsevich and Soibelman in <a href="/abs/math.SG/0011041">math.SG/0011041</a>, where we introduce a special DG category which is a key idea of our construction.}, archivePrefix = {arXiv}, author = {Kajiura, Hiroshige}, citeulike-article-id = {2277303}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0703164}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0703164}, day = {6}, eprint = {math/0703164}, keywords = {infinity\_structure}, month = {Mar}, posted-at = {2008-01-22 19:49:55}, priority = {2}, title = {An \$A\_\infty\$-structure for lines in a plane}, url = {http://arxiv.org/abs/math/0703164}, year = {2007} }

TY - ELEC ID - citeulike:2277303 L3 - citeulike-article-id:2277303 N2 - As an explicit example of an $A_\infty$-structure associated to geometry, we construct an $A_\infty$-structure for a Fukaya category of finitely many lines (Lagrangians) in $\R^2$, ie., we define also {\em non-transversal} $A_\infty$-products. This construction is motivated by homological mirror symmetry of (two-)tori, where $\R^2$ is the covering space of a two-torus. The strategy is based on an algebraic reformulation of Morse homotopy theory through homological perturbation theory (HPT) as discussed by Kontsevich and Soibelman in <a href="/abs/math.SG/0011041">math.SG/0011041</a>, where we introduce a special DG category which is a key idea of our construction. TI - An $A_\infty$-structure for lines in a plane KW - infinity_structure AU - Kajiura, Hiroshige PY - 2007/Mar/06/ UR - http://arxiv.org/abs/math/0703164 ER -