Academic literature on the topic 'Fukaya category'
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Journal articles on the topic "Fukaya category"
Castronovo, Marco. "Fukaya category of Grassmannians: Rectangles." Advances in Mathematics 372 (October 2020): 107287. http://dx.doi.org/10.1016/j.aim.2020.107287.
Full textPascaleff, James, and Nicolò Sibilla. "Topological Fukaya category and mirror symmetry for punctured surfaces." Compositio Mathematica 155, no. 3 (March 2019): 599–644. http://dx.doi.org/10.1112/s0010437x19007073.
Full textNadler, David, and Eric Zaslow. "Constructible sheaves and the Fukaya category." Journal of the American Mathematical Society 22, no. 1 (September 3, 2008): 233–86. http://dx.doi.org/10.1090/s0894-0347-08-00612-7.
Full textSheridan, Nick. "Versality of the relative Fukaya category." Geometry & Topology 24, no. 2 (September 23, 2020): 747–884. http://dx.doi.org/10.2140/gt.2020.24.747.
Full textHaydys, Andriy. "Fukaya-Seidel category and gauge theory." Journal of Symplectic Geometry 13, no. 1 (2015): 151–207. http://dx.doi.org/10.4310/jsg.2015.v13.n1.a5.
Full textLekili, Yankı, and Alexander Polishchuk. "Homological mirror symmetry for higher-dimensional pairs of pants." Compositio Mathematica 156, no. 7 (June 18, 2020): 1310–47. http://dx.doi.org/10.1112/s0010437x20007150.
Full textAbouzaid, Mohammed. "A cotangent fibre generates the Fukaya category." Advances in Mathematics 228, no. 2 (October 2011): 894–939. http://dx.doi.org/10.1016/j.aim.2011.06.007.
Full textSolomon, Jake P., and Misha Verbitsky. "Locality in the Fukaya category of a hyperkähler manifold." Compositio Mathematica 155, no. 10 (September 6, 2019): 1924–58. http://dx.doi.org/10.1112/s0010437x1900753x.
Full textAbouzaid, Mohammed. "On the wrapped Fukaya category and based loops." Journal of Symplectic Geometry 10, no. 1 (2012): 27–79. http://dx.doi.org/10.4310/jsg.2012.v10.n1.a3.
Full textAbouzaid, Mohammed. "A geometric criterion for generating the Fukaya category." Publications mathématiques de l'IHÉS 112, no. 1 (October 14, 2010): 191–240. http://dx.doi.org/10.1007/s10240-010-0028-5.
Full textDissertations / Theses on the topic "Fukaya category"
Harris, Richard. "The Fukaya category, exotic forms and exotic autoequivalences." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/242376.
Full textGanatra, Sheel (Sheel Chandrakant). "Symplectic cohomology and duality for the wrapped Fukaya Category." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73362.
Full textCataloged from PDF version of thesis.
Includes bibliographical references (p. 313-315).
Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from the Hochschild homology of W to symplectic cohomology and from symplectic cohomology to the Hochschild cohomology of W are isomorphisms, in a manner compatible with ring and module structures. This is a consequence of a more general duality for the wrapped Fukaya category, which should be thought of as a non-compact version of a Calabi-Yau structure. The new ingredients are: (1) Fourier-Mukai theory for W via a wrapped version of holomorphic quilts, (2) new geometric operations, coming from discs with two negative punctures and arbitrary many positive punctures, (3) a generalization of the Cardy condition, and (4) the use of homotopy units and A-infinity shuffle products to relate non-degeneracy to a resolution of the diagonal.
by Sheel Ganatra.
Ph.D.
Peiffer-Smadja, Amiel. "Homologies lagrangiennes, symplectiques et attachement d'anse." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS370.
Full textIn this PhD thesis, I present a new construction of the wrapped Fukaya complex of a Lagrangian and of the Chekanov algebra of a Legendrian using techniques developed by Cieliebak, Ekholm and Oancea. These constructions behave well under cobordisms and thus are fit to study the symplectic handle attachment procedure. I prove that the wrapped Fukaya complex of the cocore is isomorphic to the Chekanov algebra of the attachment sphere and show that this isomorphism factors through Abouzaid’s Open-Closed map. I then give a strategy in order to deduce from these results two important theorems announced by Bourgeois, Ekholm and Eliashberg concerning the behaviour of symplectic homology under handle attachment and the generation of the Fukaya category. In the last chapter, I define following an idea of A’Campo a geodesic flow on the skeleton of a Brieskorn manifold and relate this flow to the Reeb flow on the link of the singularity in order to try to generalize Viterbo’s isomorphism between the symplectic homology of a cotangent bundle and the homology of a loop space
Zhang, Zhongyi. "On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold." Thesis, 2020. https://doi.org/10.7916/d8-9xbk-hq04.
Full textBook chapters on the topic "Fukaya category"
Zhang, Alex Zhongyi. "Introduction to Symplectic Geometry and Fukaya Category." In Springer Proceedings in Mathematics & Statistics, 129–37. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91626-2_11.
Full text"Fukaya category and Fourier transform." In Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds, 261–74. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/amsip/023/11.
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