# Atoroidal

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## Definition of the adjective Atoroidal

What does Atoroidal mean as an attribute of a noun?

**adjective**

- [
*mathematics, of a 3-dimensional manifold*] Geometrically atoroidal.- antonym: toroidal

- [
*mathematics, of a 3-dimensional manifold*] Algebraically atoroidal.

## Explanation

**Atoroidal**: In mathematics, an atoroidal 3-manifold is one that does not contain an essential torus. There are two major variations in this terminology: a torus may be defined geometrically, as an embedded, non-boundary parallel, incompressible torus, or it may be defined algebraically, as a subgroup of its fundamental group that is not conjugate to a peripheral subgroup. The terminology is not standardized, and different authors require atoroidal 3-manifolds to satisfy certain additional restrictions.

## Printed encyclopedias and other books with definitions for Atoroidal

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### Geometric Topology (1997)

1993 Georgia International Topology Conference, August 2-13, 1993, University of Georgia, Athens, Georgia by William Hilal Kazez

*M3 is called atoroidal* if: • (geometric definition)
M contains no essential ...

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

minimal collection of disjointly EMBEDDED incompressible TORI such
that each component of the 3-MANIFOLD removed by the TORI is either "
**atoroidal**" or "Seifert-fibered." Janko Groups The SPORADIC GROUPS J1; J2; J3
and J4: The Janko group J2 is also known as the HALL-JANKO GROUP. See
also SPORADIC ...

## Online dictionaries and encyclopedias with entries for Atoroidal

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## Video about Atoroidal

**Atoroidal Meaning**

Video shows what atoroidal means. Geometrically atoroidal.. Algebraically atoroidal.. Atoroidal Meaning. How to pronounce, definition audio dictionary. How to ...

## Scrabble value of A_{1}T_{1}O_{1}R_{1}O_{1}I_{1}D_{2}A_{1}L_{1}

The value of this 9-letter word is 10 points, but it's not an accepted word in the Official Scrabble Players Dictionary.

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