Compression body

In the theory of 3-manifolds, a compression body is a kind of generalized handlebody.

A compression body is either a handlebody or the result of the following construction:

Let S be a compact, closed surface (not necessarily connected). Attach 1- handles to $S \times [0,1]$ along $S \times \{1\}$.

Let C be a compression body.

The negative boundary of C, denoted $\partial_{-}C$, is $S \times \{0\}$. (If C is a handlebody then $\partial_- C = \emptyset$.) The positive boundary of C, denoted $\partial_{+}C$, is $\partial C$ minus the negative boundary.

There is a dual construction of compression bodies starting with a surface S and attaching 2-handles to $S \times \{0\}$. In this case $\partial_{+}C$ is $S \times \{1\}$, and $\partial_{-}C$ is $\partial C$ minus the positive boundary.

Compression bodies often arise when manipulating Heegaard splittings.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometry stubs 3-manifolds Wikimedia Foundation. 2010. Игры ⚽ Поможем сделать НИР OfficeMax Danny Wuerffel Look at other dictionaries: Compression shorts — are undergarments usually worn by athletes. They are form fitting garments and when worn cover the athlete s waist to mid or lower thigh. These garments are often made from a spandex type material, similar to cycling shorts. A major benefit of… …   Wikipedia Compression sportswear — is clothing usually worn by athletes. They may be shorts, tights or underwear. They are form fitting garments and when worn cover the athlete s waist to mid or lower thigh. These garments are often made from a spandex type material. The main… …   Wikipedia Compression garment — Compression garments are pieces of clothing such as socks, pantyhose, sleeves, etc, that provide support that is especially useful for people who have to stand for long periods, or people with poor circulation. The garments can come in varying… …   Wikipedia Compression — may refer to: In physical science Compression (physical), the result of the subjection of a material to compressive stress Compression member, a class of structural elements, of which a column is the most common specific example Compressibility,… …   Wikipedia Compression tights — or Compression sportswear are specially made leggings which mold to the user s physique. They promote blood circulation and increase oxygen flow to working muscles. They also help to wick away sweat and channel moisture away from the skin. All… …   Wikipedia Body modification — (or body alteration) is the deliberate altering of the human body for any non medical reason, such as aesthetics, sexual enhancement, a rite of passage, religious reasons, to display group membership or affiliation, to create body art, shock… …   Wikipedia Body shaping — Body contouring is a general term that refers to any surgical procedure that alters different areas of the body, whether it is in a massive weight loss patient or not. Body contouring after massive weight loss refers to a series of procedures… …   Wikipedia Compression (astronomy) — Compression, in astronomy is the deviation of a heavenly body from the spherical form, called also the ellipticity. It is numerically expressed by the ratio of the differences of the axes to the major axis of the spheroid. The compression or… …   Wikipedia Compression seal fitting — A Compression seal fitting, also known as a sealing gland, is intended to seal some type of element (probe, wire, conductor, pipe, tube, fiber optic cable) when the element must pass through a pressure or environmental boundary. A compression… …   Wikipedia compression — A squeezing together; the exertion of pressure on a body in such a way as to tend to increase its density; the decrease in a dimension of a body under the action of two external forces directed toward one another in the same straight line. c. of… …   Medical dictionary 18+ © Academic, 2000-2025 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”