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Morse subsets of CAT(0) spaces are strongly contracting
1Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria.
Geometriae Dedicata
|May 9, 2020
Summary
Morse subsets in CAT(0) spaces are strongly contracting, a generalization of prior work on Morse quasi-geodesics. This finding simplifies existing results using the recurrence characterization of Morse subsets.
Area of Science:
- Geometric group theory
- Metric geometry
Background:
- Morse subsets are crucial in understanding the geometry of spaces.
- Previous work established strong contraction for Morse quasi-geodesics in CAT(0) spaces.
Purpose of the Study:
- To prove that Morse subsets of CAT(0) spaces are strongly contracting.
- To generalize and simplify existing results in geometric group theory.
Main Methods:
- Utilizing the recurrence characterization of Morse subsets.
- Developing a novel proof strategy for strong contraction properties.
Main Results:
- Demonstrated that all Morse subsets of CAT(0) spaces exhibit strong contraction.
- Provided a simplified and generalized proof compared to previous methods.
Conclusions:
- Morse subsets in CAT(0) spaces possess strong contraction properties.
- The recurrence characterization offers an effective tool for studying these properties.
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