Mathematics Colloquium



Department of Mathematics
University of Nebraska at Omaha


WHEN:
Wednesday, January 24, 2007 at 2:30 PM

WHERE:
Durham Science Center, Room 255

WHAT:


John Donnelly (Faculty Candidate)

Mount Union College


will give a talk on

Ruinous & Thin Subsets of Richard Thompson's Group F


ABSTRACT:
In the 1960's, Richard Thompson invented a triple of groups (F in T in V), which have since appeared throughout many different branches of mathematics. For example, they have provided a technique for constructing an elementary example of a finitely presented group which has unsolvable word problem, the universal obstruction to a problem in homotopy theory, the structure group for the associative law, and the first example of a group which is torsion-free, infinite dimensional, and of type infinity. The group F is conjectured to be an example of a finitely presented, nonamenable group which has no free subgroup on two generators. The speaker gives a criterion which states that F is nonamenable if and only if there exists finite subsets in F which satisfy certain properties.  


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