Complete classification of compact four-manifolds with positive isotropic curvature

By Binglong Chen, Siu-Hung Tang, Xiping Zhu. 2008

61 citations recorded by the source corpus.

In this paper, we completely classify all compact 4-manifolds with positive isotropic curvature. We show that they are diffeomorphic to $\mathbb{S}^4,$ or $\mathbb{R}\mathbb{P}^4$ or quotients of $\mathbb{S}^3\times \mathbb{R}$ by a cocompact fixed point free subgroup of the isometry group of the standard metric of $\mathbb{S}^3\times \mathbb{R}$, or a connected sum of them.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/76be32c15dead9d1487eb4814e88a5e1ab09aa41

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. S. Brendle
2. Hong-wei Xu
3. Burkhard Wilking
4. A. Malchiodi
5. J. Gu
6. Robert Haslhofer
7. S. Almaraz
8. Chao Xia

In Geometry and Topology

1. S. Brendle
2. Burkhard Wilking
3. Hong-wei Xu
4. A. Malchiodi
5. J. Gu
6. Robert Haslhofer
7. Ben Andrews
8. C. B. Ndiaye

Citations in the corpus

• Ricci flow with surgery on manifolds with positive isotropic curvature (2017, background): “For n = 4, this was proved in a landmark paper by Hamilton [20] (see also [11],[12]).”