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1.

図書

図書
Y. Eliashberg, N. Mishachev
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvii, 206 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 48
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目次情報: 続きを見る
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
Homotopy principle Open Diff $V$-invariant differential relations
Applications to closed manifolds
The homotopy principle in symplectic geometry: Symplectic and contact basics
Symplectic and contact structures on open manifolds
Symplectic and contact structures on closed manifolds
Embeddings into symplectic and contact manifolds
Microflexibility and holonomic $\mathcal{R}$-approximation
First applications of microflexibility
Microflexible $\mathfrak{U}$-invariant differential relations
Further applications to symplectic geometry
Convex integration: One-dimensional convex integration
Homotopy principle for ample differential relations
Directed immersions and embeddings
First order linear differential operators Nash-Kuiper theorem
Bibliography
Index
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
2.

図書

図書
Markus J. Pflaum
出版情報: Berlin ; Tokyo : Springer, c2001  viii, 230 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1768
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Introduction
Notation
Stratified Spaces and Functional Structures / 1:
Decomposed spaces / 1.1:
Stratifications / 1.2:
Smooth Structures / 1.3:
Local Triviality and the Whitney conditions / 1.4:
The sheaf of Whitney functions / 1.5:
Rectifiable curves and regularity / 1.6:
Extension theory for Whitney functions on regular spaces / 1.7:
Differential Geometric Objects on Singular Spaces / 2:
Stratified tangent bundles and Whitney's condition (A) / 2.1:
Derivations and vector fields / 2.2:
Differential forms and stratified cotangent bundle / 2.3:
Metrics and length space structures / 2.4:
Differential Operators / 2.5:
Poisson structures / 2.6:
Control Theory / 3:
Tubular neighborhoods / 3.1:
Cut point distance and maximal tubular neighborhoods / 3.2:
Curvature moderate submanifolds / 3.3:
Geometric implications of the Whitney conditions / 3.4:
Existence and uniqueness theorems / 3.5:
Tubes and control data / 3.6:
Controlled vector fields and integrability / 3.7:
Extension theorems on controlled spaces / 3.8:
Thom's first isotopy lemma / 3.9:
Cone spaces / 3.10:
Orbit Spaces / 4:
Differentiable <$>\cal {G}<$>-Manifolds / 4.1:
Proper Group Actions / 4.2:
Stratification of the Orbit Space / 4.3:
Functional Structure / 4.4:
DeRham-Cohomology / 5:
The deRham complex on Singular Spaces / 5.1:
DeRham cohomology on <$>\cal {C}^\infty<$>-cone Spaces / 5.2:
DeRham theorems on orbit spaces / 5.3:
DeRham cohomology of Whitney functions / 5.4:
Homology of Algebras of Smooth Functions / 6:
Topological algebras and their modules / 6.1:
Homological algebra for topological modules / 6.2:
Continuous Hochschild homology / 6.3:
Hochschild homology of algebras of smooth functions / 6.4:
Supplements from linear algebra and functional analysis / A:
The vector space distance / A.1:
Polar decomposition / A.2:
Topological tensor products / A.3:
Kahler diflferentials / B:
The space of Kähler differentials / B.1:
Topological version / B.2:
Application to locally ringed Spaces / B.3:
Jets, Whitney functions and a few <$>\cal {C}^\infty<$>-mappings / C:
Fréchet topologies for <$>\cal {C}^\infty<$>-functions / C.1:
Jets / C.2:
Whitney functions / C.3:
Smoothing of the angle / C.4:
Introduction
Notation
Stratified Spaces and Functional Structures / 1:
3.

図書

図書
Lawrence Conlon
出版情報: Boston : Birkhäuser, c2001  xii, 418 p. ; 25 cm
シリーズ名: Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft
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目次情報: 続きを見る
Preface to the Second Edition
Topological Manifolds
The Local Theory of Smooth Functions
The Global Theory of Smooth Functions
Flows and Foliations
Lie Groups and Lie Algebras
Covectors and 1--Forms
Multilinear Algebra and Tensors
Integration of Forms and de Rham Cohomology
Forms and Foliations
Riemannian Geometry
Principal Bundles
Construction of the Universal Covering
Inverse Function Theorem
Ordinary Differential Equations
The de Rham Cohomology Theorem
Bibliography
Index
Preface to the Second Edition
Topological Manifolds
The Local Theory of Smooth Functions
4.

図書

図書
Shigeyuki Morita ; translated by Teruko Nagase, Katsumi Nomizu
出版情報: Providence, R.I. : American Mathematical Society, c2001  xxiv, 321 p. ; 22 cm
シリーズ名: Translations of mathematical monographs ; v. 201
Iwanami series in modern mathematics
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5.

図書

図書
Władysław Ślebodziński
出版情報: Warszawa : Państwowe Wydawnictwo Naukowe, 1954-1963  2 v. ; 25 cm
シリーズ名: Monografie matematyczne ; t. 31, 40
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6.

図書

図書
Juan A. Navarro González, Juan B. Sancho de Salas
出版情報: Berlin ; Tokyo : Springer-Verlag, c2003  xiii, 188 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1824
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7.

図書

図書
Georges de Rham ; translated from the French by F.R. Smith ; introduction to the English edition by S.S. Chern
出版情報: Berlin ; New York : Springer-Verlag, 1984  x, 166 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 266
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8.

図書

図書
by Marston Morse
出版情報: Princeton, N.J. : Princeton University Press , [Tokyo] : University of Tokyo Press, 1976  iii, 255 p. ; 24 cm
シリーズ名: Mathematical notes ; 16
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9.

図書

図書
[by] F. Brickell and R.S. Clark
出版情報: London ; New York : Van Nostrand Reinhold, 1970  xi, 289 p. ; 24 cm
シリーズ名: The new university mathematics series
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10.

図書

図書
Louis Auslander, Robert Mackenzie
出版情報: New York ; San Francisco ; Toronto : McGraw-Hill Book Company, Inc., c1963  ix, 219 p. ; 24 cm
シリーズ名: McGraw-Hill series in higher mathematics
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