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.
The Lens Space Recognition Problem and Seifert Fiber Spaces
Kate Petersen, University of Minnesota Duluth
Authors: Neil Hoffman and Kate Petersen
2022 AWM Research Symposium
Women in Groups, Geometry, and Dynamics