Four-dimensional aspects of tight contact 3-manifolds
Abstract
A surprising result of the 20th century is that the classification problem for four-dimensional spaces called smooth 4-manifolds is more subtle and difficult than the analogous problem for both lower- and higher-dimensional spaces. Classifying 4-manifolds is intimately connected to the study of surfaces embedded therein. This article proves results and proposes conjectures relating such surfaces in 4-manifolds to three-dimensional geometric structures called contact structures.
- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- June 2021
- DOI:
- 10.1073/pnas.2025436118
- arXiv:
- arXiv:2010.13162
- Bibcode:
- 2021PNAS..11825436H
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Symplectic Geometry;
- 57K18;
- 57K10;
- 57K41;
- 57K31;
- 57R58;
- 57R65;
- 57K33;
- 53D10;
- 53D40;
- 57K40;
- 57K43
- E-Print:
- 14 pages, 1 figure