Browse
Publications
Preprints
About
About UCL Open: Env.
Aims and Scope
Editorial Board
Indexing
APCs
How to cite
Publishing policies
Editorial policy
Peer review policy
Equality, Diversity & Inclusion
About UCL Press
Contact us
For authors
Information for authors
How it works
Benefits of publishing with us
Submit
How to submit
Preparing your manuscript
Article types
Open Data
ORCID
APCs
Contributor agreement
For reviewers
Information for reviewers
Review process
How to peer review
Peer review policy
My ScienceOpen
Sign in
Register
Dashboard
Search
Browse
Publications
Preprints
About
About UCL Open: Env.
Aims and Scope
Editorial Board
Indexing
APCs
How to cite
Publishing policies
Editorial policy
Peer review policy
Equality, Diversity & Inclusion
About UCL Press
Contact us
For authors
Information for authors
How it works
Benefits of publishing with us
Submit
How to submit
Preparing your manuscript
Article types
Open Data
ORCID
APCs
Contributor agreement
For reviewers
Information for reviewers
Review process
How to peer review
Peer review policy
My ScienceOpen
Sign in
Register
Dashboard
Search
53
views
0
references
Top references
cited by
110
Cite as...
0 reviews
Review
0
comments
Comment
0
recommends
+1
Recommend
0
collections
Add to
0
shares
Share
Twitter
Sina Weibo
Facebook
Email
1,951
similar
All similar
Record
: found
Abstract
: not found
Book
: not found
Differential Topology
other
Author(s):
Morris W. Hirsch
Publication date
(Print):
1976
Publisher:
Springer New York
Read this book at
Publisher
Buy book
Review
Review book
Invite someone to review
Bookmark
Cite as...
There is no author summary for this book yet. Authors can add summaries to their books on ScienceOpen to make them more accessible to a non-specialist audience.
Related collections
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory
Author and book information
Book
ISBN (Print):
978-1-4684-9451-8
ISBN (Electronic):
978-1-4684-9449-5
Publication date (Print):
1976
DOI:
10.1007/978-1-4684-9449-5
SO-VID:
4719fcde-a7b5-4067-a9b6-faf69b17a40d
License:
http://www.springer.com/tdm
History
Data availability:
Comments
Comment on this book
Sign in to comment
Book chapters
pp. 1
The Basic Ideas
pp. 1
Notation and Prerequisites
pp. 1
Unique Factorization
pp. 1
The Classification of Random Walk
pp. 1
Manifolds
pp. 1
Introduction
pp. 1
Graphs
pp. 1
Introduction
pp. 1
Introduction
pp. 1
Introduction
pp. 1
Introduction
pp. 1
Algebraic Geometry
pp. 1
Fundamental Number-Theoretic Algorithms
pp. 1
Smooth Manifolds
pp. 1
Prerequisites
pp. 3
Convex Bodies
pp. 3
Generalities on linear representations
pp. 3
Finite Fields
pp. 3
Affine Group Schemes
pp. 3
Representations of Finite Groups
pp. 3
Affine and Projective Varieties
pp. 5
Elliptic Functions
pp. 5
Elliptic and Modular Functions
pp. 5
Algebraic Varieties
pp. 7
Categories, Functors, and Natural Transformations
pp. 7
Manifolds and Maps
pp. 9
Sets and Classes
pp. 10
Character theory
pp. 10
Convex Sets
pp. 11
p-Adic Fields
pp. 12
Characters
pp. 12
Topological Vector Spaces
pp. 13
Affine Group Schemes: Examples
pp. 17
Regular Functions and Maps
pp. 17
Applications of Unique Factorization
pp. 19
Hilbert Symbol
pp. 21
Representations
pp. 21
Algebraic Curves
pp. 23
Homomorphisms
pp. 25
Subgroups, products, induced representations
pp. 26
Examples; Induced Representations; Group Algebras; Real Representations
pp. 27
Quadratic Forms over Q p and over Q
pp. 28
Congruence
pp. 28
Algebraic Matrix Groups
pp. 29
The Modular Function
pp. 29
Combinatorial theory of polytopes and polyhedral sets
pp. 30
Measures and Outer Measures
pp. 31
Fock Spaces
pp. 31
Constructions on Categories
pp. 32
Cones, Projections, and More About Products
pp. 32
Compact groups
pp. 33
Examples and Constructions
pp. 33
Sheaf Cohomology
pp. 34
Function Spaces
pp. 35
Examples
pp. 35
Polytopes
pp. 39
The Structure of U(ℤ/nℤ)
pp. 39
Subgraphs
pp. 39
Irreducible and Connected Components
pp. 41
The Geometry of Elliptic Curves
pp. 41
Families and Parameter Spaces
pp. 43
Fourier Expansions
pp. 44
Representations of $${\mathfrak{S}_{_d}}$$ : Young Diagrams and Frobenius’s Character Formula
pp. 45
The Geometry of Elliptic Curves
pp. 45
Algorithms for Linear Algebra and Lattices
pp. 46
Connected Components and Separable Algebras
pp. 47
The group algebra
pp. 48
Integral Quadratic Forms with Discriminant ± 1
pp. 48
Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz
pp. 49
Extension of Measures
pp. 50
Quadratic Reciprocity
pp. 51
The Modular Equation
pp. 51
Affine Algebraic Groups
pp. 53
Tensors and Differential Forms
pp. 54
Groups of Multiplicative Type
pp. 54
Induced representations; Mackey’s criterion
pp. 54
Harmonic Analysis
pp. 55
Universals and Limits
pp. 61
Examples
pp. 61
Higher Levels
pp. 61
The Theorem on Arithmetic Progressions
pp. 61
Examples of induced representations
pp. 62
Unipotent Groups
pp. 63
Representations of $${\mathfrak{U}_d}$$ and $$G{L_2}\left( {{\mathbb{F}_q}} \right)$$
pp. 63
Grassmannians and Related Varieties
pp. 65
The Action of a Permutation Group
pp. 65
Polyhedral spheres
pp. 65
Lie Algebras
pp. 66
Quadratic Gauss Sums
pp. 67
Transversality
pp. 68
Artin’s theorem
pp. 68
Jordan Decomposition
pp. 72
Rational Functions and Rational Maps
pp. 73
Nilpotent and Solvable Groups
pp. 73
Measurable Functions
pp. 74
A theorem of Brauer
pp. 75
Weyl’s Construction
pp. 75
Automorphisms of the Modular Function Field
pp. 77
Modular Forms
pp. 79
Homogeneous Spaces
pp. 79
Adjoints
pp. 79
Finite Fields
pp. 79
Connected Graphs
pp. 80
Fundamental Properties and Constructions
pp. 81
Lie Groups
pp. 81
Applications of Brauer’s theorem
pp. 83
Differentials
pp. 85
Vector Bundles and Tubular Neighborhoods
pp. 87
Characteristic 0 Theory
pp. 88
More Examples
pp. 88
Gauss and Jacobi Sums
pp. 89
Results from Algebraic Number Theory
pp. 90
Rationality questions
pp. 92
Lie Algebras
pp. 93
Lie Groups
pp. 95
Semisimple and Unipotent Elements
pp. 95
Complex Multiplication
pp. 95
Integration
pp. 98
Determinantal Varieties
pp. 99
Trees
pp. 102
Rationality questions: examples
pp. 103
Minkowski sum and mixed volume
pp. 103
Faithful Flatness
pp. 104
Lie Algebras and Lie Groups
pp. 105
Two-Dimensional Recurrent Random Walk
pp. 106
The Structure of a Primitive Group
pp. 108
Algorithms on Polynomials
pp. 108
Cubic and Biquadratic Reciprocity
pp. 109
Limits
pp. 109
Faithful Flatness of Hopf Algebras
pp. 109
Polytopes with Few Vertices
pp. 109
Solvable Groups
pp. 110
The Formal Group of an Elliptic Curve
pp. 111
Reduction of Elliptic Curves
pp. 114
Quotient Maps
pp. 114
Algebraic Groups
pp. 115
The groups RK(G), R k (G), and P k (G)
pp. 117
Nonseparable Graphs
pp. 117
General Set Functions
pp. 120
Degrees, Intersection Numbers, and the Euler Characteristic
pp. 121
Construction of Quotients
pp. 121
Initial Classification of Lie Algebras
pp. 123
Complex Multiplication
pp. 124
The cde triangle
pp. 130
Elliptic Curves over Finite Fields
pp. 131
Descent Theory Formalism
pp. 131
Theorems
pp. 133
Definitions of Dimension and Elementary Examples
pp. 133
Lie Algebras in Dimensions One, Two, and Three
pp. 133
Borel Subgroups
pp. 135
Tree-Search Algorithms
pp. 136
Neighborly Polytopes
pp. 137
Monads and Algebras
pp. 137
Integration on Manifolds
pp. 137
Product Spaces
pp. 138
Equations over Finite Fields
pp. 138
Proofs
pp. 140
Descent Theory Computations
pp. 142
Morse Theory
pp. 143
Bounds on Orders of Permutation Groups
pp. 143
Lattice polytopes and fans
pp. 146
Representations of sl2ℂ
pp. 146
Elliptic Curves over ℂ
pp. 146
Euler’s Relation
pp. 147
Modular characters
pp. 147
Borel Subgroups; Reductive Groups
pp. 147
Centralizers of Tori
pp. 147
Families of Dynamical Systems
pp. 149
Shimura’s Reciprocity Law
pp. 151
Algorithms for Algebraic Number Theory I
pp. 151
The Zeta Function
pp. 151
More Dimension Computations
pp. 157
Flows in Networks
pp. 159
Applications to Artin representations
pp. 159
Linear Differential Equations
pp. 161
The Function Δ(ατ)/Δ(τ)
pp. 161
Transformations and Functions
pp. 161
Analogues of Euler’s Relation
pp. 161
Representations of sl3ℂ, Part I
pp. 161
Monoids
pp. 161
Sheaves, Cohomology, and the de Rham Theorem
pp. 163
Structure of Reductive Groups
pp. 163
Hilbert Polynomials
pp. 169
Cobordism
pp. 171
Elliptic Curves over Local Fields
pp. 171
The ι-adic and p-adic Representations of Deuring
pp. 172
Algebraic Number Theory
pp. 173
Complexity of Algorithms
pp. 173
Fourier Series
pp. 174
Random Walk on a Half-Line
pp. 174
Smoothness and Tangent Spaces
pp. 175
Representations ofsl3ℂ, Part II: Mainly Lots of Examples
pp. 177
Isotopy
pp. 177
The Mathieu Groups and Steiner Systems
pp. 184
Probability
pp. 186
Gauss Maps, Tangential and Dual Varieties
pp. 187
Elliptic Surfaces
pp. 187
Ihara’s Theory
pp. 188
Quadratic and Cyclotomic Fields
pp. 188
Surfaces
pp. 188
Representations and Classification of Semisimple Groups
pp. 189
Elliptic Curves over Global Fields
pp. 191
Abelian Categories
pp. 192
Extremal Problems Concerning Numbers of Faces
pp. 197
The General Setup: Analyzing the Structure and Representations of an Arbitrary Semisimple Lie Algebra
pp. 197
The Tate Parametrization
pp. 199
Toric Varieties
pp. 200
Tangent Spaces to Grassmannians
pp. 203
The Stickelberger Relation and the Eisenstein Reciprocity Law
pp. 205
The Isogeny Theorems
pp. 205
Connectivity
pp. 210
Multiply Transitive Groups
pp. 211
Further Topics Involving Smoothness and Tangent Spaces
pp. 211
Special Limits
pp. 211
sl4ℂ and slnℂ
pp. 216
Locally Compact Spaces
pp. 217
Survey of Rationality Properties
pp. 218
Algorithms for Quadratic Fields
pp. 219
The Hodge Theorem
pp. 221
Division Points over Number Fields
pp. 223
Properties of Boundary Complexes
pp. 224
Degree
pp. 228
Bernoulli Numbers
pp. 233
Kan Extensions
pp. 237
Random Walk on an Interval
pp. 238
Symplectic Lie Algebras
pp. 239
Further Examples and Applications of Degree
pp. 239
Product Expansions
pp. 241
Integral Points on Elliptic Curves
pp. 243
Planar Graphs
pp. 249
Dirichlet L-functions
pp. 250
Haar Measure
pp. 251
Symmetry and Braidings in Monoidal Categories
pp. 251
k-Equivalence of Polytopes
pp. 251
Singular Points and Tangent Cones
pp. 253
sp6ℂ and sp2nℂ
pp. 255
The Structure of the Symmetric Groups
pp. 259
The Siegel Functions and Klein Forms
pp. 259
Sheaves and projective toric varieties
pp. 263
3-Polytopes
pp. 266
Measure and Topology in Groups
pp. 266
Parameter Spaces and Moduli Spaces
pp. 267
Structures in Categories
pp. 267
The Kronecker Limit Formulas
pp. 267
Orthogonal Lie Algebras
pp. 269
Diophantine Equations
pp. 274
Transient Random Walk
pp. 274
Examples and Applications of Infinite Permutation Groups
pp. 275
Arithmetic Hyperbolic 3-Manifolds and Orbifolds
pp. 276
Computing the Mordell-Weil Group
pp. 279
The First Limit Formula and L-series
pp. 279
Books on Nonstandard Analysis
pp. 282
so6ℂ, so7ℂ and somℂ
pp. 282
Quadrics
pp. 287
The Four-Colour Problem
pp. 287
The Second Limit Formula and L-series
pp. 289
The Néron Model
pp. 295
Stable Sets and Cliques
pp. 297
Elliptic Curves
pp. 297
Algorithms for Algebraic Number Theory II
pp. 299
Spin Representations of $$\mathfrak{s}{\mathfrak{d}_m}\mathbb{C}$$
pp. 307
Cohomology of toric varieties
pp. 319
The Classification of Complex Simple Lie Algebras
pp. 319
The Mordell-Weil Theorem
pp. 329
The Probabilistic Method
pp. 329
Angle-sums Relations; the Steiner Point
pp. 339
g2 and Other Exceptional Lie Algebras
pp. 339
New Progress in Arithmetic Geometry
pp. 343
Recurrent Random Walk
pp. 347
Graph Minors
pp. 350
Addition and Decomposition of Polytopes
pp. 357
Vertex Colourings
pp. 360
Introduction to Elliptic Curves
pp. 366
Complex Lie Groups; Characters
pp. 379
Diameters of Polytopes
pp. 391
Colourings of Maps
pp. 396
Long Paths and Circuits on Polytopes
pp. 399
Weyl Character Formula
pp. 408
Elliptic Curves over Complete Fields
pp. 412
Factoring in the Dark Ages
pp. 413
Matchings
pp. 415
More Character Formulas
pp. 430
Real Lie Algebras and Lie Groups
pp. 432
Arrangements of Hyperplanes
pp. 437
Modern Primality Tests
pp. 451
Edge Colourings
pp. 454
Local Height Functions
pp. 455
Concluding Remarks
pp. 459
Matrix Rings, Categories of Modules, and Morita Theory
pp. 469
Modern Factoring Methods
pp. 471
Hamilton Cycles
pp. 503
Coverings and Packings in Directed Graphs
pp. 527
Electrical Networks
pp. 557
Integer Flows and Coverings
Similar content
1,951
Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies
Authors:
Patricio Salgado-Rebolledo
,
Fabrizio Canfora
A Divide-And-Conquer Method for computing the Betti numbers of Finite Topological Spaces
Authors:
Patrick Erik Bradley
Towards the prediction of essential genes by integration of network topology, cellular localization and biological process information
Authors:
Marcio Acencio
,
Ney Lemke
See all similar
Cited by
103
Convex Computation of the Region of Attraction of Polynomial Control Systems
Authors:
Milan Korda
,
Didier Henrion
The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
Authors:
Francois Lekien
,
Shane D. Ross
Stability regions of nonlinear autonomous dynamical systems
Authors:
F.F. Wu
,
M.W. Hirsch
,
H.-D. Chiang
See all cited by