Handlebody
Sign in to saveright|thumb|A genus three handlebody. In the mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces. Handlebodies play an important role in Morse theory, cobordism theory and the surgery theory of high-dimensional manifolds. Handles are used to particularly study 3-manifolds.
Wikidata facts
- Subclass of
- manifold
Show 1 more fact
- maintained by WikiProject
- WikiProject Mathematics
Sources (2)
via Wikidata · CC0
~4 min read
Encyclopedic overview
5 sectionsContents
- ''n''-dimensional handlebodies
- 3-dimensional handlebodies
- Examples
- See also
- References
right|thumb|A genus three handlebody. In the mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces. Handlebodies play an important role in Morse theory, cobordism theory and the surgery theory of high-dimensional manifolds. Handles are used to particularly study 3-manifolds.
Handlebodies play a similar role in the study of manifolds as simplicial complexes and CW complexes play in homotopy theory, allowing one to analyze a space in terms of individual pieces and their interactions.
Excerpted from Wikipedia’s “Handlebody” article, available under the CC BY-SA 4.0 licence.