On the complex analytic theory of riemann surfaces and planar discontinuous groups

Zieschang, Heiner; Vogt, Elmar; Coldewey, Hans-Dieter

doi:10.1007/bfb0089698

Search citation statements

Order By: Relevance

Paper Sections

Select...

For Each F Denote By1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let p be the genus of the surface S and g be the genus of the modular surface Σ. It follows from the Riemann -Hurwitz formula (see, for example, [25]) that…”

Section: For Each F Denote Bymentioning

confidence: 99%

On a Classification of Periodic Maps on the 2-Torus

Baranov¹,

Grines²,

Pochinka³

et al. 2023

Nelin. Dinam.

View full text Add to dashboard Cite

In this paper, following J. Nielsen, we introduce a complete characteristic of orientation-preserving periodic maps on the two-dimensional torus. All admissible complete characteristics were found and realized. In particular, each of the classes of orientation-preserving periodic homeomorphisms on the 2-torus that are nonhomotopic to the identity is realized by an algebraic automorphism. Moreover, it is shown that the number of such classes is finite. According to V. Z. Grines and A. Bezdenezhnykh, any gradient-like orientation-preserving diffeomorphism of an orientable surface is represented as a superposition of the time-1 map of a gradient-like flow and some periodic homeomorphism. Thus, the results of this work are directly related to the complete topological classification of gradient-like diffeomorphisms on surfaces.

show abstract

“…Let p be the genus of the surface S and g be the genus of the modular surface Σ. It follows from the Riemann -Hurwitz formula (see, for example, [25]) that…”

Section: For Each F Denote Bymentioning

confidence: 99%