Noncommutative homological mirror functor / Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau.
| Author/creator | Cho, Cheol-Hyun |
| Other author | Hong, Hansol. |
| Other author | Lau, Siu-Cheong. |
| Format | Electronic |
| Publication Info | Providence, RI : American Mathematical Society, [2021] |
| Description | v, 116 pages : illustrations ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; number 1326 |
| Contents | A-infinity algebra over a noncommutative base -- Noncommutative mirror from a single Lagrangian and the centrality theorem -- The mirror functor from a single Lagrangian -- Elliptic curves and deformation quantizations -- Mirror construction using several Lagrangians and quiver algebras -- Finite group symmetry and graded mirror functors -- 4-punctured spheres and the pillowcase -- Extended mirror functor -- Mirror construction for punctured Riemann surface -- Mirrors of Calabi-Yau threefolds associated with quadratic differentials. |
| Abstract | "We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural functor from the Fukaya category to the category of matrix factorizations of the constructed Landau-Ginzburg model. As applications, it is applied to elliptic orbifolds, punctured Riemann surfaces and certain non-compact Calabi-Yau threefolds to construct their mirrors and functors. In particular it recovers and strengthens several interesting results of Etingof-Ginzburg, Bocklandt and Smith, and gives a unified understanding of their results in terms of mirror symmetry and symplectic geometry. As an interesting application, we construct an explicit global deformation quantization of an affine del Pezzo surface as a noncommutative mirror to an elliptic orbifold"-- Provided by publisher. |
| General note | "May 2021, volume 271, number 1326 (third of 7 numbers)." |
| Bibliography note | Includes bibliographical references. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2022007632 |
| ISBN | 9781470447618 (paperback) |
| ISBN | (epub) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |