Mathematics Colloquia and Seminars

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The Andrews-Curtis conjecture (1965) is an open conjecture in low dimensional topology. It was originally conceived with the hope of finding a counterexample to the 3 and 4 dimensional Poincare conjecture. Since the proof of the Poincare conjecure, the Andrews-Curtis conjecture is thought to be false (though this hasn't been shown). However, there is no consensus on the validity of the generalized Andrews-Curtis conjecture. This generalization admits a description in purely algebraic terms, as well as a more common topological interpretation. In this talk, both descriptions will be explained, and also an introduction to simple homotopy equivalence will be given.