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Comparing topologies on the Morse boundary and quasi-isometry invariance
- Publication Year :
- 2019
-
Abstract
- We compare several topologies on the Morse boundary $\partial_M Y$ of a $\mathrm{CAT(0)}$ cube complex $Y$. In particular, we show that the two topologies introduced by Cashen and Mackay are not equal in general and provide a new description of one of them in the language of cube complexes. As a corollary, we obtain a new approach to tackle the question whether the visual topology induces a quasi-isometry-invariant topology on the Morse boundary. This leads to an obstruction to quasi-isometry-invariance in terms of the behaviour of geodesics under quasi-isometries.<br />Comment: 27 pages, 4 figures, comments welcome
- Subjects :
- Mathematics - Group Theory
Mathematics - General Topology
20F65
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1903.07048
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10711-020-00553-3