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Atoroidal

Definition of the adjective Atoroidal

What does Atoroidal mean as an attribute of a noun?

adjective

  1. [mathematics, of a 3-dimensional manifold] Geometrically atoroidal.
  2. [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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Google previewGeometric 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 ...

Google previewCRC 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 ...

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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 A1T1O1R1O1I1D2A1L1

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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