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A new invariant of 4-manifolds

Published Web Location

https://doi.org/10.1073/pnas.1718953115
Abstract

We define an integer invariant [Formula: see text] of a smooth, compact, closed 4-manifold X by minimizing a certain complexity of a trisection of X over all trisections. The good feature of [Formula: see text] is that when [Formula: see text] and X is a homology 4-sphere, then X is diffeomorphic to the 4-sphere. Naturally, L is hard to compute.

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