Gromov-Hausdorff Limits of Closed Surfaces
Tobias Dott
TL;DR
This paper characterizes the limits of sequences of closed surfaces under Gromov-Hausdorff convergence, providing a complete description of the possible limit spaces within this class.
Contribution
It offers a comprehensive description of the Gromov-Hausdorff closure for all length spaces homeomorphic to a fixed closed surface, filling a gap in geometric topology.
Findings
Complete description of Gromov-Hausdorff limits for closed surfaces.
Identification of possible limit spaces within the class.
Clarification of the structure of limits in geometric topology.
Abstract
We completely describe the Gromov-Hausdorff closure of the class of length spaces being homeomorphic to a fixed closed surface.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Topology and Set Theory · Holomorphic and Operator Theory