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University of Sydney Algebra Seminar

Nancy Scherich

Friday 25 October, 12-1pm, Place: Carslaw 275

An algorithm to Detect Non-Order Preserving Braids

This grad student friendly talk will be in the intersection of algebra in topology. We will start with an introduction of the braid groups and the notion of group orderability. Viewing the braid group as a subgroup of the automorphism group of the free group, we can ask if a braid preserves a bi-order of the free group, or not. We will learn how this notion of order preserving plays an interesting role in knot theory and 3-manifold theory. We will conclude with a new algorithm to detect when a braid is not considered order preserving and see some consequences of this algorithm.