## Geometry and Topology

•  Barry Minemyer, The Ohio State University
•  Real hyperbolic hyperplane complements in the complex hyperbolic plane
•  12/08/2016
•  2:00 PM - 2:50 PM
•  C304 Wells Hall

In the late 80's Gromov and Thurston constructed examples of manifolds which do not admit a hyperbolic metric but do admit metrics whose sectional curvature is pinched arbitrarily close to -1. Their construction involves taking cyclic branched covers of hyperbolic manifolds over 'nice' codimension two totally geodesic submanifolds. In a joint project with J.F. Lafont, J. Meyer, and B. Tshishiku we have extended this construction to 4-manifolds whose metric is modeled on the complex hyperbolic plane. This will be the content of the first half of the talk. For this group project, I needed to understand the metric in the complex hyperbolic plane expressed in polar coordinates about a copy of the real hyperbolic plane. This research will make up the second half of the talk.

## Contact

Department of Mathematics
Michigan State University