Smooth embeddings

Depends on

• Immersions, submersions, and constant-rank maps
• Homeomorphism, open map, closed map, embedding, and what it means for a property to be topological
• Subspace topology: the traces of the open sets, its closed sets and its bases, the continuity of the inclusion, and the characteristic property of a map into a subspace

Used by

• A proper injective immersion is an embedding Corollary
• An injective immersion from a compact manifold is an embedding Corollary
• Compatible tubular neighbourhoods agree near compact sets up to ambient isotopy Corollary
• Embedding obstructions include all immersion normal-class obstructions Corollary
• High-dimensional simply connected h-cobordant manifolds are diffeomorphic Corollary
• Homotopy spheres of dimension at least five bounding a contractible manifold are standard spheres Corollary
• Isotopic embeddings of a compact manifold have diffeomorphic complements Corollary
• A reflected sphere embedding is regularly homotopic but not isotopic to the standard one Counterexample
• An immersed disk in the four-ball cannot always be cleaned relative to its boundary Counterexample
• Vanishing stable characteristic classes do not make two embeddings isotopic Counterexample
• Curves and geometric intersection numbers on the marked disk Definition
• Framed cobordism of framed submanifolds Definition
• Framed embedded surgery sphere Definition
• Framings of a normal bundle Definition
• h-Cobordism Definition
• Handle slide of one k handle over another Definition
• Immersed, embedded, and closed Lie subgroups Definition
• Oriented links in the three-sphere and ambient isotopy Definition
• Reeb components of a codimension-one foliation Definition
• Secant and tangent direction maps of a Euclidean embedding Definition
• Self-transverse immersions and the double point locus Definition
• Smooth isotopies, diffeotopies and ambient isotopies Definition
• Stable normal inverse of the tangent bundle Definition
• Taut codimension-one foliations Definition
• The closure of a geometric braid Definition
• The local Whitney move Definition
• Tubular neighbourhoods of embedded submanifolds Definition
• Whitney circle for a pair of intersection points Definition
• Whitney disk, clean Whitney disk and framed Whitney disk Definition
• A local Whitney move in Euclidean space Example
• Boy's surface: an immersion of the real projective plane in three-space Example
• Compact isotopic submanifolds have isomorphic normal bundles and diffeomorphic complements Example
• Extending a visible isotopy of an unknotted circle in ℝ³ Example
• Oppositely signed intersections of two three-manifolds in a simply connected six-manifold Example
• An injective immersion need not be an embedding False statement
• A co-oriented closed transversal detects nonvanishing rational homology of a compact leaf Lemma
• A double point has two disjoint embedded sheet disks meeting transversely Lemma
• A non-closed leaf of a codimension-one foliation meets a closed transversal Lemma
• A smooth isotopy of a compact manifold extends to an ambient isotopy Lemma
• Arcs joining two points of a connected submanifold avoiding finitely many points Lemma

…and 29 more results.

Dependency tree · two levels

10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Will J. Merry, Differential Geometry, Definition 6.1 (standard reference, not scraped)
• John M. Lee, Introduction to Smooth Manifolds, Embeddings (standard reference, not scraped)