Kate Petersen, University of Minnesota Duluth
Authors: Neil Hoffman and Kate Petersen
2022 AWM Research Symposium
Women in Groups, Geometry, and Dynamics

The Lens Space Recognition Problem is the problem of deciding whether a given 3-manifold is a lens space (including S^3). A decision problem is said to lie in NP if an affirmative solution can be verified via certificate in polynomial time relative to the input size (of a triangulation in this case) and we say that a problem lies in coNP if a negative solution can be verified by such a certificate. I will discuss these types of decision problems in the context of low-dimensional topology. The Lens Space Recognition problem is known to lie in NP by work of Lackenby and Schleimer. I will present recent progress, namely that for Seifert fiber spaces the Lens Space Recognition Problem lies in coNP. This is joint work with Neil Hoffman.

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