Lagrangian Floer Theory and Its Deformations

Lagrangian Floer Theory and Its Deformations
Title Lagrangian Floer Theory and Its Deformations PDF eBook
Author Yong-Geun Oh
Publisher Springer Nature
Pages 426
Release
Genre
ISBN 9819717981

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Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory

Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory
Title Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory PDF eBook
Author Kenji Fukaya
Publisher American Mathematical Soc.
Pages 282
Release 2019-09-05
Genre Mathematics
ISBN 1470436256

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In this paper the authors first develop various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations, i.e., deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology. Essentially the same kind of construction is independently carried out by Usher in a slightly less general context. Then the authors explore various applications of these enhancements to the symplectic topology, especially new construction of symplectic quasi-states, quasi-morphisms and new Lagrangian intersection results on toric and non-toric manifolds. The most novel part of this paper is its use of open-closed Gromov-Witten-Floer theory and its variant involving closed orbits of periodic Hamiltonian system to connect spectral invariants (with bulk deformation), symplectic quasi-states, quasi-morphism to the Lagrangian Floer theory (with bulk deformation). The authors use this open-closed Gromov-Witten-Floer theory to produce new examples. Using the calculation of Lagrangian Floer cohomology with bulk, they produce examples of compact symplectic manifolds which admits uncountably many independent quasi-morphisms . They also obtain a new intersection result for the Lagrangian submanifold in .

Noncommutative Homological Mirror Functor

Noncommutative Homological Mirror Functor
Title Noncommutative Homological Mirror Functor PDF eBook
Author Cheol-Hyun Cho
Publisher American Mathematical Society
Pages 116
Release 2021-09-24
Genre Mathematics
ISBN 1470447614

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View the abstract.

Lagrangian Intersection Floer Theory

Lagrangian Intersection Floer Theory
Title Lagrangian Intersection Floer Theory PDF eBook
Author Kenji Fukaya
Publisher American Mathematical Soc.
Pages 410
Release 2010-06-28
Genre Mathematics
ISBN 0821852493

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This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.

Geometry and Physics of Branes

Geometry and Physics of Branes
Title Geometry and Physics of Branes PDF eBook
Author U Bruzzo
Publisher CRC Press
Pages 232
Release 2002-11-05
Genre Science
ISBN 1000687694

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Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theo

Modern Geometry

Modern Geometry
Title Modern Geometry PDF eBook
Author Vicente Muñoz
Publisher American Mathematical Soc.
Pages 426
Release 2018-09-05
Genre Mathematics
ISBN 1470440946

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This book contains a collection of survey articles of exciting new developments in geometry, written in tribute to Simon Donaldson to celebrate his 60th birthday. Reflecting the wide range of Donaldson's interests and influence, the papers range from algebraic geometry and topology through symplectic geometry and geometric analysis to mathematical physics. Their expository nature means the book acts as an invitation to the various topics described, while also giving a sense of the links between these different areas and the unity of modern geometry.

Geometry and Physics: Volume I

Geometry and Physics: Volume I
Title Geometry and Physics: Volume I PDF eBook
Author Jørgen Ellegaard Andersen
Publisher Oxford University Press
Pages 400
Release 2018-10-18
Genre Mathematics
ISBN 0192522361

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Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.