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K-State Today

February 23, 2017

Mathematics Colloquium Lecture Feb. 23

By Reta McDermott

Alex Zupan, University of Nebraska, will present "The Andrews-Curtis Conjecture and the Topology of the 4-Sphere" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, Feb. 23, in 122 Cardwell Hall.

The abstract for the lecture is: The Andrews-Curtis Conjecture — which recently celebrated its 50th birthday — asserts that every balanced presentation of the trivial group can be reduced to the trivial presentation via a sequence of moves which preserve the number or relators and generators. Although there are a number of prominent potential counterexamples, the conjecture is still considered wide open. We will discuss how the Andrews-Curtis Conjecture relates to an open problem about handle decompositions of the standard smooth 4-sphere, along with strategies for the simplification of these tricky cases. Much of the material in this talk is joint work with Jeffrey Meier.