Anomalous Expansive Homeomorphisms on Surfaces
Published:Dec 31, 2025 15:01
•1 min read
•ArXiv
Analysis
This paper addresses a question about the existence of certain types of homeomorphisms (specifically, cw-expansive homeomorphisms) on compact surfaces. The key contribution is the construction of such homeomorphisms on surfaces of higher genus (genus >= 0), providing an affirmative answer to a previously posed question. The paper also provides examples of 2-expansive but not expansive homeomorphisms and cw2-expansive homeomorphisms that are not N-expansive, expanding the understanding of these properties on different surfaces.
Key Takeaways
- •Provides an affirmative answer to a question about the existence of cw-expansive homeomorphisms.
- •Constructs examples on surfaces of higher genus.
- •Offers new examples of 2-expansive but not expansive homeomorphisms.
- •Presents examples of cw2-expansive homeomorphisms that are not N-expansive.
Reference
“The paper constructs cw-expansive homeomorphisms on compact surfaces of genus greater than or equal to zero with a fixed point whose local stable set is connected but not locally connected.”