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3. Angle structures and hyperbolic $3$-manifolds with totally geodesic boundary

Author

Zhang, Faze, Qiu, Ruifeng, and Yang, Tian

Subjects
Mathematics - Geometric Topology, 57M50
Abstract

This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and conversely each hyperbolic $3$-manifold with totally geodesic boundary has an ideal triangulation that admits angle structures., Comment: 11 pages, 4 figures, some references are added

Published
2014

10. The subset of not realizing metrics on the curve complex.

Author

Zhang, Faze and Zou, Yanqing

Subjects
*SET theory, *MATRICES (Mathematics), *TOPOLOGY, *TORUS, *KNOT theory
Abstract

In [F. Zhang, R. Qiu and Y. Zou, The subset of realizing metrics on the curve complex, Topology Appl. 193 (2015) 259-269], they defined a subset of and a metric through each point of for the curve complex . For further understanding the curve complex, we concern the whole set . With adaption to the flow theory on torus, we prove that for any point of , the is not a metric on or . This means that the is the maximal subset of realizing metrics on the curve complex. [ABSTRACT FROM AUTHOR]

Published
2017
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