# Introduction to Smooth Manifolds

```@inproceedings{Lee2002IntroductionTS,
title={Introduction to Smooth Manifolds},
author={John M. Lee},
year={2002}
}```
Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves and Flows.- 10 Vector Bundles.- 11 The Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem.- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22…
2,619 Citations

## Figures from this paper

An introduction to manifolds
A Brief Introduction.- Part I. The Euclidean Space.- Smooth Functions on R(N).- Tangent Vectors In R(N) as Derivations.- Alternating K-Linear Functions.- Differential Forms on R(N).- Part II.
Introduction to differential and Riemannian geometry
• Mathematics
• 2020
This chapter introduces the basic concepts of differential geometry: Manifolds, charts, curves, their derivatives, and tangent spaces. The addition of a Riemannian metric enables length and angle
Integration on Manifolds
• Mathematics
• 2013
After giving some definitions and results on orientability of smooth manifolds, the problems treated in the present chapter are concerned with orientation of smooth manifolds; especially the
An introduction to Hamilton and Perelman's work on the conjectures of Poincaré and Thurston
• Mathematics
• 2006
Preface 3 Introduction 4 1 The Topology Setting 8 1.1 The Poincare conjecture 8 1.2 Some examples of 3-dimensional manifolds 9 1.3 The Sphere (or Prime) Decomposition 13 1.4 The Torus Decomposition
Notes on the Riemannian Geometry of Lie Groups
Lie groups occupy a central position in modern differential geometry and physics, as they are very useful for describing the continuous symmetries of a space. This paper is an expository article
Introduction to manifolds
• L. Tu
• Computer Science
• 2007
The theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics, and one of the most basic topological invariants of a manifold, its de Rham cohomology is computed.
Symmetries on manifolds: generalizations of the radial lemma of Strauss
• Mathematics
Revista Matemática Complutense
• 2018
For a compact subgroup G of the group of isometries acting on a Riemannian manifold M we investigate subspaces of Besov and Triebel–Lizorkin type which are invariant with respect to the group action.
Lq,p -Cohomology of Riemannian Manifolds and Simplicial Complexes of Bounded Geometry
The Lq,p-cohomology of a Riemannian manifold (M, g) is defined to be the quotient of closed Lp-forms, modulo the exact forms which are derivatives of Lq-forms, where the measure considered comes from
The cohomology rings of seven dimensional primitive cohomogeneity one manifolds
approved: Christine M. Escher A striking feature in the study of Riemannian manifolds of positive sectional curvature is the narrowness of the collection of known examples. In this thesis, we examine
Jet Prolongations of Fibered Manifolds
This chapter introduces fibered manifolds and their jet prolongations. First, we recall properties of differentiable mappings of constant rank and introduce, with the help of rank, the notion of a

## References

SHOWING 1-10 OF 41 REFERENCES
Introduction to Topological Manifolds
Preface.- 1 Introduction.- 2 Topological Spaces.- 3 New Spaces from Old.- 4 Connectedness and Compactness.- 5 Cell Complexes.- 6 Compact Surfaces.- 7 Homotopy and the Fundamental Group.- 8 The
Symplectic structures on Banach manifolds
1. Normal form. Let M be a Banach manifold. A symplectic structure on M is a closed 2-form Q such that the associated mapping S: T(M)->T*(M) defined by Q(X) = X _ ] 0 is a bundle isomorphism. If M is
Functions of Several Variables
1 Euclidean spaces.- 1.1 The real number system.- 1.2 Euclidean En.- 1.3 Elementary geometry of En.- 1.4 Basic topological notions in En.- *1.5 Convex sets.- 2 Elementary topology of En.- 2.1
Obstructions to the smoothing of piecewise-differentiable homeomorphisms
Since the publication in 1956 of John Milnor's fundamental paper [l ] in which he constructs differentiable structures on S7 nondiffeomorphic to the standard one, several further results concerning
Riemannian Manifolds: An Introduction to Curvature
What Is Curvature?.- Review of Tensors, Manifolds, and Vector Bundles.- Definitions and Examples of Riemannian Metrics.- Connections.- Riemannian Geodesics.- Geodesics and Distance.- Curvature.-
Topology of 4-manifolds
• Mathematics
• 1990
One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological
On the parallelizability of the spheres
• Mathematics
• 1958
is always divisible by (2k — 1)!. I wonder if you have noted the connection of this result with classical problems, such as the existence of division algebras, and the parallelizability of spheres.
Topology and geometry
Preface 1. General Topology 2. Diferentiable Manifolds 3. 1= Fundamental Group 4. Homology Theory 5. Cohomology 6. Products and Duality 7. Homotopy Theory Appendices A-E Bibliography Index of Symbols
Principles of mathematical analysis
Chapter 1: The Real and Complex Number Systems Introduction Ordered Sets Fields The Real Field The Extended Real Number System The Complex Field Euclidean Spaces Appendix Exercises Chapter 2: Basic
Elements of algebraic topology
Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in