Metric weak proper discontinuity for pseudo-Anosov maps

Q: What type of study is this?

This is a Quantitative Study study.

In-Hyeok Choi

doi:10.48550/arxiv.2506.21214

June 26, 2025Open Access

Metric weak proper discontinuity for pseudo-Anosov maps

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Key Points

The study defines a new metric weak proper discontinuity for pseudo-Anosov maps on surfaces, expanding existing theories.
It reveals that numerous quasi-morphisms exist in the homeomorphism group of both tori and hyperbolic surfaces, indicating complex behavior.
The application to homeomorphisms reveals their unbounded nature concerning fixed sets, showcasing deeper geometric properties.
The findings could impact the understanding of dynamical systems by emphasizing interactions between geometry and algebra of maps.

Implication

This research introduces a metric weak proper discontinuity for pseudo-Anosov maps, highlighting quasi-morphisms in the homeomorphism group.

Abstract

We present a metric version of weak proper discontinuity (WPD) for pseudo-Anosov maps on surfaces. As an application, we show that there are plenty of quasi-morphisms on the homeomorphism group of a torus or a hyperbolic surface that are unbounded on certain homeomorphisms with large fixed set.

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Cite This Study

In-Hyeok Choi (2025) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06e7dd https://doi.org/10.48550/arxiv.2506.21214

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Metric weak proper discontinuity for pseudo-Anosov maps

Key Points

Implication

Abstract

Discussion

Cite This Study

Metric weak proper discontinuity for pseudo-Anosov maps

Key Points

Implication

Abstract

Discussion

Cite This Study

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