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200 10$aDifferential forms on Wasserstein space and infinite-dimensional Hamiltonian systems /$fWilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2010.
210  4$dİ2010
215   $a1 online resource (77 p.)
225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 211, Number 993
300   $a"Volume 211, Number 993 (third of 5 numbers)."
311   $a0-8218-4939-5 
320   $aIncludes bibliographical references.
327   $a""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. The topology on M and a differential calculus of curves""; ""2.1. The space of distributions""; ""2.2. The topology on M""; ""2.3. Tangent spaces and the divergence operator""; ""2.4. Analytic justification for the tangent spaces""; ""Chapter 3. The calculus of curves, revisited""; ""3.1. Embedding the geometry of RD into M""; ""3.2. The intrinsic geometry of M""; ""3.3. Embedding the geometry of M into (Cc)*""; ""3.4. Further comments""; ""Chapter 4. Tangent and cotangent bundles""
327   $a""4.1. Push-forward operations on M and TM""""4.2. Differential forms on M""; ""4.3. Discussion""; ""Chapter 5. Calculus of pseudo differential 1-forms""; ""5.1. Green's formula for smooth surfaces and 1-forms""; ""5.2. Regularity and differentiability of pseudo 1-forms""; ""5.3. Regular forms and absolutely continuous curves""; ""5.4. Green's formula for annuli""; ""5.5. Example: 1-forms on the space of discrete measures""; ""5.6. Discussion""; ""Chapter 6. A symplectic foliation of M""; ""6.1. The group of Hamiltonian diffeomorphisms""; ""6.2. A symplectic foliation of M""
327   $a""6.3. Algebraic properties of the symplectic distribution""""Chapter 7. The symplectic foliation as a Poisson structure""; ""7.1. Review of Poisson geometry""; ""7.2. The symplectic foliation of M, revisited""; ""Appendix A. Review of relevant notions of Differential Geometry""; ""A.1. Calculus of vector fields and differential forms""; ""A.2. Lie groups and group actions""; ""A.3. Cohomology and invariant cohomology""; ""A.4. The group of diffeomorphisms""; ""Bibliography""
410  0$aMemoirs of the American Mathematical Society ;$vVolume 211, Number 993.
606   $aDifferential forms
606   $aHamiltonian systems
606   $aInfinite-dimensional manifolds
615  0$aDifferential forms.
615  0$aHamiltonian systems.
615  0$aInfinite-dimensional manifolds.
676   $a515/.39
700   $aGangbo$b Wilfrid$041092
702   $aKim$b Hwa Kil
702   $aPacini$b Tommaso$f1971-
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910827648403321
996   $aDifferential forms on Wasserstein space and infinite-dimensional Hamiltonian systems$93981275
997   $aUNINA