Fake 4-ball

Mathematical topological manifold

In mathematics, a fake 4-ball is a compact contractible topological 4-manifold. Michael Freedman proved that every three-dimensional homology sphere bounds a fake 4-ball. His construction involves the use of Casson handles and so does not work in the smooth category.

References

Alexandru Scorpan, The Wild World of 4-Manifolds, American Mathematical Society, ISBN 0-8218-3749-4

Manifolds (Glossary)

Basic concepts

Topological manifold
- Atlas
Differentiable/Smooth manifold
- Differential structure
- Smooth atlas
Submanifold
Riemannian manifold
Smooth map
Submersion
Pushforward
Tangent space
Differential form
Vector field

Main results (list)

Maps

Curve
Diffeomorphism
- Local
Geodesic
Exponential map
- in Lie theory
Foliation
Immersion
Integral curve
Lie derivative
Section
Submersion

Types of
manifolds

Tensors

Vectors	Distribution Lie bracket Pushforward Tangent space bundle Torsion Vector field Vector flow
Covectors	Closed/Exact Covariant derivative Cotangent space bundle De Rham cohomology Differential form Vector-valued Exterior derivative Interior product Pullback Ricci curvature flow Riemann curvature tensor Tensor field density Volume form Wedge product
Bundles	Adjoint Affine Associated Cotangent Dual Fiber (Co) Fibration Jet Lie algebra (Stable) Normal Principal Spinor Subbundle Tangent Tensor Vector
Connections	Affine Cartan Ehresmann Form Generalized Koszul Levi-Civita Principal Vector Parallel transport