An $A_\infty$-structure for lines in a plane
| dc.creator | Kajiura, Hiroshige | |
| dc.date | 2007-03-06 | |
| dc.date.accessioned | 2026-07-07T07:50:27Z | |
| dc.date.available | 2026-07-07T07:50:27Z | |
| dc.description | 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 math.SG/0011041, where we introduce a special DG category which is a key idea of our construction. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703164 | |
| dc.identifier | http://arxiv.org/abs/math/0703164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125171 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Symplectic Geometry | |
| dc.title | An $A_\infty$-structure for lines in a plane | |
| dc.type | text |