English

Open manifolds with uniformly positive isotropic curvature

Differential Geometry 2023-11-28 v1 Analysis of PDEs Geometric Topology

Abstract

We prove the following result: Let (M,g0)(M,g_0) be a complete noncompact manifold of dimension n12n\geq 12 with isotropic curvature bounded below by a positive constant, with scalar curvature bounded above, and with injectivity radius bounded below. Then there is a finite collection X\mathcal{X} of spherical nn-manifolds and manifolds of the form Sn1×R/G\mathbb{S}^{n-1} \times \mathbb{R} /G, where GG is a discrete subgroup of the isometry group of the round cylinder Sn1×R\mathbb{S}^{n-1}\times \mathbb{R}, such that MM is diffeomorphic to a (possible infinite) connected sum of members of X\mathcal{X}. This extends a recent work of Huang. The proof uses Ricci flow with surgery on open orbifolds with isolated singularities.

Keywords

Cite

@article{arxiv.2311.15825,
  title  = {Open manifolds with uniformly positive isotropic curvature},
  author = {Hong Huang},
  journal= {arXiv preprint arXiv:2311.15825},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:1909.12265