# cap off

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## English[edit]

### Verb[edit]

**cap off** (*third-person singular simple present* **caps off**, *present participle* **capping off**, *simple past and past participle* **capped off**)

- (transitive) To finish by making one last addition.
- (mathematics, transitive) To glue a relatively uncomplicated compact manifold to a manifold of the same dimension along (a component of the latter's boundary).
*a.***1997**, Rob[ion] Kirby, "Problems in Low-Dimensional Topology", problem 3.21, in, 1997, William H[ilal] Kazez, editor,*Geometric Topology*, proceedings of the 1993 Georgia International Topology Conference, AMS/IP Studies in Advanced Mathematics 2, American Mathematical Society, →ISBN, part 2, page 163,- Let be an acyclic 2-complex and an abstract regular neighborhood of ; , so
**cap off**to get a homology -sphere .

- Let be an acyclic 2-complex and an abstract regular neighborhood of ; , so
*a.***1997**, Michael T. Anderson, "Scalar Curvature and Geometrization Conjectures for 3-Manifolds", in, 1997, Karsten Grove and Peter Petersen, editors,*Comparison Geometry*, Mathematical Sciences Research Institute Publications 30, →ISBN, page 53,- Note, however, that when one cuts a 3-manifold along an incompressible torus, there is no canonical way to
**cap off**the boundary components thus created, as is the case for spheres. For any toral boundary component, there are many ways to glue in a solid torus... .

- Note, however, that when one cuts a 3-manifold along an incompressible torus, there is no canonical way to
**1997**, W[illiam] B[ernard] Raymond Lickorish,*An Introduction to Knot Theory*, Graduate Texts in Mathematics 175, Springer, →ISBN, page 61,**Cap off**, with discs just above the annulus, any circuits that bound in the annulus; then use annuli to**cap off**adjacent pairs of curves that encircle the annulus in opposite directions.