Spectral Invariants With Bulk Quasi Morphisms And Lagrangian Floer Theory
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Author |
: Kenji Fukaya |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 282 |
Release |
: 2019-09-05 |
ISBN-10 |
: 9781470436254 |
ISBN-13 |
: 1470436256 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory by : Kenji Fukaya
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 .
Author |
: Yong-Geun Oh |
Publisher |
: Springer Nature |
Total Pages |
: 426 |
Release |
: |
ISBN-10 |
: 9789819717989 |
ISBN-13 |
: 9819717981 |
Rating |
: 4/5 (89 Downloads) |
Synopsis Lagrangian Floer Theory and Its Deformations by : Yong-Geun Oh
Author |
: Vicente Muñoz |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 426 |
Release |
: 2018-09-05 |
ISBN-10 |
: 9781470440947 |
ISBN-13 |
: 1470440946 |
Rating |
: 4/5 (47 Downloads) |
Synopsis Modern Geometry by : Vicente Muñoz
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.
Author |
: Christopher L Douglas |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 111 |
Release |
: 2020-02-13 |
ISBN-10 |
: 9781470437718 |
ISBN-13 |
: 1470437716 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Cornered Heegaard Floer Homology by : Christopher L Douglas
Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.
Author |
: Massimiliano Berti |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 171 |
Release |
: 2020-04-03 |
ISBN-10 |
: 9781470440695 |
ISBN-13 |
: 1470440695 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves by : Massimiliano Berti
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
Author |
: Harold Rosenberg |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 62 |
Release |
: 2020-09-28 |
ISBN-10 |
: 9781470441852 |
ISBN-13 |
: 1470441853 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Degree Theory of Immersed Hypersurfaces by : Harold Rosenberg
The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.
Author |
: Pavel M. Bleher |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 144 |
Release |
: 2020-09-28 |
ISBN-10 |
: 9781470441845 |
ISBN-13 |
: 1470441845 |
Rating |
: 4/5 (45 Downloads) |
Synopsis The Mother Body Phase Transition in the Normal Matrix Model by : Pavel M. Bleher
In this present paper, the authors consider the normal matrix model with cubic plus linear potential.
Author |
: Zhaobing Fan |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 123 |
Release |
: 2020-09-28 |
ISBN-10 |
: 9781470441753 |
ISBN-13 |
: 1470441756 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Affine Flag Varieties and Quantum Symmetric Pairs by : Zhaobing Fan
The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.
Author |
: Rodney G. Downey |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 90 |
Release |
: 2020-09-28 |
ISBN-10 |
: 9781470441623 |
ISBN-13 |
: 1470441624 |
Rating |
: 4/5 (23 Downloads) |
Synopsis Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees by : Rodney G. Downey
First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.
Author |
: Andrew J. Blumberg |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 100 |
Release |
: 2020-09-28 |
ISBN-10 |
: 9781470441784 |
ISBN-13 |
: 1470441780 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Localization for $THH(ku)$ and the Topological Hochschild and Cyclic Homology of Waldhausen Categories by : Andrew J. Blumberg
The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.