English

On the generalized Geroch conjecture for complete spin manifolds

Differential Geometry 2022-12-08 v2 General Relativity and Quantum Cosmology

Abstract

Let WW be a closed area enlargeable manifold in the sense of Gromov-Lawson and MM be a noncompact spin manifold, we show that the connected sum M#WM\# W admits no complete metric of positive scalar curvature. When W=TnW=T^n, this provides a positive answer to the generalized Geroch conjecture in the spin setting.

Keywords

Cite

@article{arxiv.2204.09184,
  title  = {On the generalized Geroch conjecture for complete spin manifolds},
  author = {Xiangsheng Wang and Weiping Zhang},
  journal= {arXiv preprint arXiv:2204.09184},
  year   = {2022}
}

Comments

4 pages, title changed, the published version

R2 v1 2026-06-24T10:52:43.007Z