Fukaya categories and picard–lefschetz theory

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August undefined, 2024

WebDec 2, 2009 · Download PDF Abstract: We prove that the derived Fukaya category of the Lefschetz fibration defined by a Brieskorn-Pham polynomial is equivalent to the triangulated category of singularities associated with the same polynomial together with a grading by an abelian group of rank one. Symplectic Picard-Lefschetz theory developed by Seidel is … WebApr 13, 2011 · P. Seidel, Fukaya categories and deformations, in “Proceedings of the International Congress of Mathematicians II (Beijing, 2002)”, Higher Ed. Press, Beijing (2002), 351–360. P. Seidel, Fukaya Categories and Picard–Lefschetz Theory, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2008.

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WebMar 30, 2016 · We will not use a specific text for this course. Below are some general references on Fukaya categories, Lagrangian (and Hamiltonian) Floer homology, and J-holomorphic curves. P. Seidel, Fukaya categories and Picard-Lefschetz theory. Available for purchase here (or on Amazon, etc.). D. Auroux, A beginner's introduction to Fukaya … WebFigure 2: The procedure for designating interior nodes as forgettable or unforgettable, and boundary nodes as puncturable or unpuncturable. On the top left we illustrate an element of Rk,Kpun,`,`for,i . All nodes are drawn as a solid point; solid interior marked points are unforgettable; grey interior marked points are forgettable; open boundary marked points … family guy healthbars

The Fukaya category of the punctured 2-torus - University …

WebFukaya categories and Picard-Lefschetz theory (Lemma 2.1) Fukaya categories and Picard-Lefschetz theory (Section 8g) Fukaya categories and Picard-Lefschetz … WebNov 2, 2015 · Download Citation Picard–Lefschetz theory and dilating ℂ*-actions We consider ${\\mathbb C}^*$-actions on Fukaya categories of exact symplectic manifolds. … Web8 rows · Fukaya Categories and Picard-Lefschetz Theory. The central objects in the book are Lagrangian ... family guy heart and soul

$[math/0206155] Fukaya categories and deformations$

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WebJun 15, 2008 · Fukaya Categories and Picard-Lefschetz Theory (Zurich Lectures in Advanced Mathematics) The central objects in the book are Lagrangian submanifolds … WebIn mathematics, Picard–Lefschetz theory studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold. It was introduced … family guy health psaWebAs Fukaya categories are A ∞-categories, they have associated derived categories, which are the subject of the celebrated homological mirror symmetry conjecture of … cooking travel

"WebFeb 24, 2010 · submanifolds of M, and the morphisms in the category are the chain complexes CF(L 0,L 1) which underlie the Floer homology groups. Donaldson’s category is recovered on passing to homology (in this context, called passing to the derived … " - Fukaya categories and picard–lefschetz theory

Fukaya categories and picard–lefschetz theory

WebFeb 2, 2011 · Abstract. We prove that the derived Fukaya category of the Lefschetz fibration defined by a Brieskorn–Pham polynomial is equivalent to the triangulated category of singularities associated with the same polynomial together with a grading by an abelian group of rank one. Symplectic Picard-Lefschetz theory developed by Seidel is an … WebWhat has a Fukaya category? A Liouville domain M. [Reference: P. Seidel, Fukaya categories and Picard{Lefschetz theory, 2008] What is it? An A 1-category F(M), linear over an arbitrary ground eld K. What it’s not. In studying the Fukaya category, methods of ‘pure’ category theory (adjoint functors, limits, etc.) are of little use.

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WebJul 22, 2024 · The paper contains a certain amount of material that may be of interest independently of the exact sequence: in particular, chapter 1 covers "symplectic Picard-Lefschetz theory" in some detail ... WebNov 2, 2015 · Download Citation Picard–Lefschetz theory and dilating ℂ*-actions We consider ${\\mathbb C}^*$-actions on Fukaya categories of exact symplectic manifolds. Such actions can be constructed ...

WebThe relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. WebMar 28, 2014 · Picard–Lefschetz theory and dilating ℂ*-actions. November 2015 · Journal of Topology. Paul Seidel. We consider $ {\mathbb C}^*$-actions on Fukaya categories of exact symplectic manifolds ...

Web6 rows · Jun 15, 2008 · This item: Fukaya Categories and Picard-Lefschetz Theory (Zurich Lectures in Advanced Mathematics) ... WebJun 15, 2008 · Fukaya Categories and Picard-Lefschetz Theory (Zurich Lectures in Advanced Mathematics) The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve …

WebFukaya Categories And Picard Lefschetz Theory Book PDFs/Epub. Download and Read Books in PDF "Fukaya Categories And Picard Lefschetz Theory" book is now available, Get the book in PDF, Epub and Mobi for Free. Also available Magazines, Music and other Services by pressing the "DOWNLOAD" button, create an account and enjoy unlimited. ...

WebMar 29, 2024 · We give a definition of Seidel's `relative Fukaya category', for a smooth complex projective variety, under a semipositivity assumption. We use the Cieliebak--Mohnke approach to transversality via stabilizing divisors. ... Fukaya Categories and Picard-Lefschetz Theory. P. Seidel; Mathematics. 2008; 788. View 2 excerpts, … family guy heart monitorWeb"The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya … family guy heart attackWebJun 26, 2008 · The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity … cooking travel classes