PreprintCC BY-NC-SA 4.0arXiv
The recognition problem for 4-manifolds and the unknotting problem for 2-spheres in 4-manifolds
Abstract
We show that there is no algorithm to decide whether or not a given 4-manifold is PL homeomorphic to the connected sum of 7 copies of S 2 x S 2 . We also show that the TOP and PL unknotting problems for all surfaces in the connected sum of 7 copies of S 2 x S 2 are unsolvable.
Related
- The unknotting problem for surfaces in the 4-sphere
- Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature
- Brieskorn spheres bound orbit spaces of torus manifolds
- Smooth manifolds homotopy equivalent to products of spheres
- New families of moment-angle manifolds diffeomorphic to connected sums of products of spheres
BibTeX
@misc{gordon2026recognition,
title = {{The recognition problem for 4-manifolds and the unknotting problem for 2-spheres in 4-manifolds}},
author = {Cameron Gordon},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00355},
eprint = {2611.00355},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00355},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The recognition problem for 4-manifolds and the unknotting problem for 2-spheres in 4-manifolds
AU - Cameron Gordon
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00355
UR - https://arxiv.org/abs/2611.00355
AB - We show that there is no algorithm to decide whether or not a given 4-manifold is PL homeomorphic to the connected sum of 7 copies of S 2 x S 2 . We also show that the TOP and PL unknotting problems for all surfaces in the connected sum of 7 copies of S 2 x S 2 are unsolvable.
ER -