Year: 2026
Type: preprint
Abstract: We prove that two invariants of smooth 4-manifolds defined in terms of trisections are uncomputable: the trisection genus and the Kirby-Thompson L-invariant. That is, there does not exist an algorithm that takes as input a triangulated closed orientable 4-manifold and outputs one of these quantities. The result on the L-invariant resolves the second part of Problem 4.116 in the K3 problem list. In the same spirit, we show that the PL multisection genus of PL manifolds is uncomputable in dimensions at least four.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204803326