Atnaujinkite slapukų nuostatas

El. knyga: Symplectic Topology and Floer Homology: Volume 2, Floer Homology and its Applications

4.00/5 (4 ratings by Goodreads)
(Pohang University of Science and Technology, Republic of Korea)
  • Formatas: PDF+DRM
  • Serija: New Mathematical Monographs
  • Išleidimo metai: 27-Aug-2015
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781316383193
Kitos knygos pagal šią temą:
Symplectic Topology and Floer Homology: Volume 2, Floer Homology and its ApplicationsDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: New Mathematical Monographs
  • Išleidimo metai: 27-Aug-2015
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781316383193
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

Published in two volumes, this is the first book to provide a systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory.

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. The first volume covered the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.

Recenzijos

'This volume completes a comprehensive introduction to symplectic topology and Floer theory.' Hansjorg Geiges, Mathematical Reviews

Daugiau informacijos

The second part of a two-volume set offering a systematic explanation of symplectic topology. This volume provides a comprehensive introduction to Hamiltonian and Lagrangian Floer theory.
Contents of Volume 1 ix
Preface xiii
PART 3 LAGRANGIAN INTERSECTION FLOER HOMOLOGY
12 Floer homology on cotangent bundles
3(38)
12.1 The action functional as a generating function
4(3)
12.2 L2-gradient flow of the action functional
7(4)
12.3 C0 bounds of Floer trajectories
11(4)
12.4 Floer-regular parameters
15(1)
12.5 Floer homology of submanifold S ⊂ N
16(7)
12.6 Lagrangian spectral invariants
23(10)
12.7 Deformation of Floer equations
33(3)
12.8 The wave front and the basic phase function
36(5)
13 The off-shell framework of a Floer complex with bubbles
41(32)
13.1 Lagrangian subspaces versus totally real subspaces
41(2)
13.2 The bundle pair and its Maslov index
43(4)
13.3 Maslov indices of polygonal maps
47(3)
13.4 Novikov covering and Novikov ring
50(3)
13.5 Action functional
53(2)
13.6 The Maslov--Morse index
55(2)
13.7 Anchored Lagrangian submanifolds
57(3)
13.8 Abstract Floer complex and its homology
60(4)
13.9 Floer chain modules
64(9)
14 On-shell analysis of Floer moduli spaces
73(36)
14.1 Exponential decay
73(9)
14.2 Splitting ends of M(x, y; B)
82(11)
14.3 Broken cusp-trajectory moduli spaces
93(4)
14.4 Chain map moduli space and energy estimates
97(12)
15 Off-shell analysis of the Floer moduli space
109(41)
15.1 Off-shell framework of smooth Floer moduli spaces
109(6)
15.2 Off-shell description of the cusp-trajectory spaces
115(4)
15.3 Index calculation
119(3)
15.4 Orientation of the moduli space of disc instantons
122(5)
15.5 Gluing of Floer moduli spaces
127(13)
15.6 Coherent orientations of Floer moduli spaces
140(10)
16 Floer homology of monotone Lagrangian submanifolds
150(32)
16.1 Primary obstruction and holomorphic discs
150(6)
16.2 Examples of monotone Lagrangian submanifolds
156(5)
16.3 The one-point open Gromov--Witten invariant
161(5)
16.4 The anomaly of the Floer boundary operator
166(10)
16.5 Product structure; triangle product
176(6)
17 Applications to symplectic topology
182(37)
17.1 Nearby Lagrangian pairs: thick--thin dichotomy
183(5)
17.2 Local Floer homology
188(6)
17.3 Construction of the spectral sequence
194(8)
17.4 Biran and Cieliebak's theorem
202(6)
17.5 Audin's question for monotone Lagrangian submanifolds
208(3)
17.6 Polterovich's theorem on Ham(S2)
211(8)
PART 4 HAMILTONIAN FIXED-POINT FLOER HOMOLOGY
18 The action functional and the Conley--Zehnder index
219(25)
18.1 Free loop space and its S1 action
220(1)
18.2 The free loop space of a symplectic manifold
221(7)
18.3 Perturbed action functionals and their action spectrum
228(5)
18.4 The Conley--Zehnder index of [ z, w]
233(7)
18.5 The Hamiltonian-perturbed Cauchy--Riemann equation
240(4)
19 Hamiltonian Floer homology
244(37)
19.1 Novikov Floer chains and the Novikov ring
244(4)
19.2 Definition of the Floer boundary map
248(6)
19.3 Definition of a Floer chain map
254(2)
19.4 Construction of a chain homotopy map
256(2)
19.5 The composition law of Floer chain maps
258(3)
19.6 Transversality
261(7)
19.7 Time-reversal flow and duality
268(10)
19.8 The Floer complex of a small Morse function
278(3)
20 The pants product and quantum cohomology
281(33)
20.1 The structure of a quantum cohomology ring
282(7)
20.2 Hamiltonian fibrations with prescribed monodromy
289(10)
20.3 The PSS map and its isomorphism property
299(13)
20.4 Frobenius pairing and duality
312(2)
21 Spectral invariants: construction
314(34)
21.1 Energy estimates and Hofer's geometry
315(7)
21.2 The boundary depth of the Hamiltonian H
322(2)
21.3 Definition of spectral invariants and their axioms
324(8)
21.4 Proof of the triangle inequality
332(5)
21.5 The spectrality axiom
337(5)
21.6 Homotopy invariance
342(6)
22 Spectral invariants: applications
348(60)
22.1 The spectral norm of Hamiltonian diffeomorphisms
349(3)
22.2 Hofer's geodesics and periodic orbits
352(14)
22.3 Spectral capacities and sharp energy--capacity inequality
366(6)
22.4 Entov and Polterovich's partial symplectic quasi-states
372(9)
22.5 Entov and Polterovich's Calabi quasimorphism
381(16)
22.6 Back to topological Hamiltonian dynamics
397(6)
22.7 Wild area-preserving homeomorphisms on D2
403(5)
Appendix A The Weitzenbock formula for vector-valued forms 408(4)
Appendix B The three-interval method of exponential estimates 412(5)
Appendix C The Maslov index, the Conley--Zehnder index and the index formula 417(12)
References 429(15)
Index 444
Yong-Geun Oh is Director of the IBS Center for Geometry and Physics and is Professor in the Department of Mathematics at POSTECH (Pohang University of Science and Technology) in Korea. He was also Professor in the Department of Mathematics at the University of Wisconsin, Madison. He is a member of the KMS, the AMS, the Korean National Academy of Sciences, and the inaugural class of AMS Fellows. In 2012 he received the Kyung-Ahm Prize for Science in Korea.
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97813163831932e.html
Raktažodžiai: