Math News July 20th, 2009
Patrick Stein

An aggregation of some of the math blogs that I follow.

Math News: Items from date 2012-04-05 (1 - 1 of about 1) (xml) (Feedlist)

Exciting News on Three Dimensional ManifoldsGil Kalai
(05.04.2012 04:36h)

The Virtually Haken Conjecture A Haken 3-manifold is a compact 3-dimensional manifold M which is irreducible in a certain strong sense but contains an incompressible surface S. An embedded surface S is incompressible if the embedding indices an injection of its fundamental group to the fundamental group of M. A 3-manifold is virtually finite Haken if it has a finite cover which is Haken. This is a typical way how the word “virtually” occurs in algebra and topology. The virtually Haken conjecture states that every compact, orientable, irreducible 3-dimensional manifold with infinite fundamental group is virtually Haken. The big news ... [Link]

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