A sequence of increasingly complicated examples

Andrew Donald

Friday 18th November, 2011 16:00-17:00 Mathematics Building, room 516

Abstract

Two different representations of the same object look entirely unrelated. For example, it is not always easy to determine if a pair of knot diagrams describe equivalent knots or if two finite group presentations give isomorphic groups. In both of these cases however, theoretical result guarantee that any equivalence can be seen via a sequence of 'obvious' equivalences. A property or invariant defined from a diagram extends to a property of the object provided it is preserved by these moves. This gives a way of distinguishing between inequivalent diagrams. I will explore this idea via a sequence of increasingly complicated examples.

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