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1.

図書

図書
Martin R. Bridson, André Haefliger
出版情報: Berlin ; Tokyo : Springer, c1999  xxi, 643 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 319
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2.

図書

図書
edited by Keith M. Ball, Vitali Milman
出版情報: New York : Cambridge University Press, c1999  xx, 236 p. ; 25 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 34
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3.

図書

図書
by Anastasios Mallios
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1998  xvii, 441 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 439 . Geometry of vector sheaves : an axiomatic approach to differential geometry ; v. 1
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目次情報: 続きを見る
General Preface (to both Volumes, I, II)
Preface (to Volume I)
Acknowledgements
Contents of Volume II
Vector Sheaves. General Theory / Part 1:
Sheaf Theory / Chapter I.:
Preliminaries. Definitions / 1.:
Sections of a sheaf / 2.:
A sheaf is its sections. Defining families of sections / 3.:
Examples. Germs and sheaves / 4.:
The sheaf of germs of locally constant functions. The constant sheaf / 4.(a).:
The sheaf of germs of continuous functions / 4.(b).:
Sheaves of germs of C[superscript infinity]-functions and of holomorphic ones / 4.(c).:
Presheaves. Basic definitions / 5.:
Morphisms of presheaves / 6.:
Stalks of a presheaf. Sheafification, or sheaf generated by a presheaf / 7.:
The sheafification functor / 8.:
Presheaf of sections of a sheaf. The section functor / 9.:
Further examples of presheaves / 10.:
The constant presheaf / 10.(a).:
Presheaves of functions / 10.(b).:
Complete presheaves. Examples / 11.:
Morphisms of presheaves (contn'd) / 12.:
The section functor and its (left) adjoint: The sheafification functor (contn'd) / 13.:
Change of base space / 14.:
The direct image (or push-out) functor / 14.(a).:
Inverse image (or pull-back) functor / 14.(b).:
Sheaves and Presheaves with Algebraic Structure / Chapter II.:
Preliminaries. Basic definitions
Sheaves with algebraic structures. A-modules / 1.(a).:
Presheaves with algebraic structure. A-presheaves / 1.(b).:
Section-wise definition of algebraic structure in a given sheaf (of sets) / 1.(c).:
A-morphisms. Exact sequences
Morphisms of A-presheaves / 2.(a).:
Quotients of A-modules / 2.(b).:
The (left) exactness of the section functor / 2.(c).:
Change of base space. The direct, resp. inverse, image functors for A-modules and A-presheaves / 2.(d).:
Direct (or Whitney) sum of A-modules. Free A-modules
Locally free A-modules. Vector sheaves
Tensor products of A-modules
The functor Hom[subscript A]
Sheaf Cohomology / 6.(a).:
Preliminaries. Fundamental concepts
Derived functors
Derived functor cohomology
Cech cohomology
The directed set of (proper) open coverings of a given topological space
Cech cochain complex
Passage to the limit
Leray's Theorem / 4.(d).:
Lifting of cocycles
Passage to the limit (of liftable cocycles) / 5.(a).:
Long exact sequences in Cech cohomology (contn'd) / 5.(b).:
Cech cohomolgy with coefficients in a presheaf
Long exact (Cech) cohomology sequence for presheaves
Cech cohomology for presheaves on paracompact spaces / 6.(b).:
Cohomology of double complexes. Hypercohomology
Cech hypercohomology / 7.(a).:
Cohomology theories in action. (Interrelations)
Fine resolutions. De Rham cohomology / 8.(a).:
The functors Ext[subscript A] and Ext[subscript A]
The functor Ext[subscript A] / 9.(a).:
A-extensions / 9.(b).:
Ext[superscript 1 subscript A] and A-extensions
The 1st cohomology set
0-dimensional (non-abelian) cohomology / 11.(a).:
Linear and Multilinear Algebra of Vector Sheaves / Chapter IV.:
Classical group sheaves
A (full) matrix algebra sheaf
The general linear group sheaf
An example
Free A-modules (contn'd)
Matrix representations of A-morphisms / 3.(a).:
The determinant morphism
Dual A-modules
Certain basic formulae relating the functors Hom[subscript A] and Hom[subscript A]
Exterior algebra of A-modules
Determinant line sheaf
Riemannian A-modules
Positive partitions of unity
Hermitian A-modules
Gram-Schmidt orthogonalization
Volume element
The Hodge (or * -) operator
Vector Sheaves and Cohomology / Chapter V.:
Vector sheaves and 1-cocycles / 1:
Section-wise definition of being a vector sheaf locally free
Cohomological classification of vector sheaves
Geometrical meaning of the 1st cohomology set (a la Grothendieck)
Examples
Behaviour of vector sheaves in cohomology
Line sheaves. The Picard group
The determinant morphism (contn'd)
Flat vector sheaves
Line sheaves and Chern classes
The functors Ext[subscript A] and Ext[subscript A] (contn'd)
Splittings of A-extensions (contn'd)
Dual A-extensions
Classical group sheaves (contn'd)
The orthogonal group sheaf
The unitary group sheaf
Category jargon / Appendix.:
Bibliography
Notational Index
Subject Index
General Preface (to both Volumes, I, II)
Preface (to Volume I)
Acknowledgements
4.

図書

図書
by Anastasios Mallios
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1998  xxi, 436 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 439 . Geometry of vector sheaves : an axiomatic approach to differential geometry ; v. 2
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5.

図書

図書
Sorin Dragomir, Liviu Ornea
出版情報: Boston : Birkhäuser, c1998  xi, 327 p. ; 25 cm
シリーズ名: Progress in mathematics ; vol. 155
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6.

図書

図書
John Roe
出版情報: Harlow : Longman, 1998  209 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 395
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7.

図書

図書
N.P. Landsman
出版情報: New York : Springer, c1998  xix, 529 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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8.

図書

図書
R.W. Sharpe ; foreword by S.S. Chern
出版情報: New York : Springer, c1997  xix, 421 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 166
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目次情報: 続きを見る
In the Ashes of the Ether: Differential Topology
Looking for the Forest in the Leaves: Folations
The Fundamental Theorem of Calculus
Shapes Fantastic: Klein Geometries
Shapes High Fantastical: Cartan Geometries
Riemannian Geometry
Mwbius Geometry
Projective Geometry
In the Ashes of the Ether: Differential Topology
Looking for the Forest in the Leaves: Folations
The Fundamental Theorem of Calculus
9.

図書

図書
John K. Beem, Paul E. Ehrlich, Kevin L. Easley
出版情報: New York : Marcel Dekker, c1996  xiv, 635 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 202
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Introduction - Riemannian themes in Lorentzian geometry
connections and curvature
Lorentzian manifolds and causality
Lorentzian distance
examples of space-times
completness and extendibility
stability of completeness and incompleteness
maximal geodesics and causally disconnected space-times
the Lorentzian cut locus
Morse index theory on Lorentzian manifolds
some results in global Lorentzian geometry
singularities
gravitational plane wave space-times
the splitting problem"
Introduction - Riemannian themes in Lorentzian geometry
connections and curvature
Lorentzian manifolds and causality
10.

図書

図書
A.T. Fomenko ; translated from the Russian by R.S. Wadhwa
出版情報: New York ; Tokyo : Gordon and Breach, 1995  xv, 467 p. ; 24 cm
シリーズ名: Advanced studies in contemporary mathematics ; v. 5
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