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Graph manifolds as ends of negatively curved Riemannian manifolds
- Source :
- Geom. Topol. 24 (2020) 2035-2074
- Publication Year :
- 2019
-
Abstract
- Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the $\Bbb H^2 \times \Bbb R$ geometry. Assume that the pieces are glued by isometries. Then, there exists a complete Riemannian metric on $\Bbb R \times M$ which is an "eventually warped cusp metric" with the sectional curvature $K$ satisfying $-1 \le K <0$. A theorem by Ontaneda then implies that $M$ appears as an end of a 4-dimensional, complete, non-compact Riemannian manifold of finite volume with sectional curvature $K$ satisfying $-1 \le K <0$.<br />Comment: Added Lemma 2.4 and Lemma 3.8 as a piece of the argument for the curvature estimate that was missing from the previous versions
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Journal :
- Geom. Topol. 24 (2020) 2035-2074
- Publication Type :
- Report
- Accession number :
- edsarx.1903.07216
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2140/gt.2020.24.2035