Automorphisms of Kronrod-Reeb graphs of Morse functions on 2-torus

TL;DR

This paper characterizes specific automorphism subgroups of Kronrod-Reeb graphs associated with Morse functions on the 2-torus, revealing their structure and symmetries.

Contribution

It provides a complete description of automorphism subgroups of Kronrod-Reeb graphs arising from diffeomorphisms preserving Morse functions on the 2-torus.

Findings

Full classification of these automorphism subgroups

Identification of symmetries induced by diffeomorphisms

Insights into the structure of Morse functions on the 2-torus

Abstract

This paper is devoted to the study of special subgroups of the automorphism groups of Kronrod-Reeb graphs of a Morse functions on $2$-torus $T^2$ which arise from the action of diffeomorphisms preserving a given Morse function on $T^2$. In this paper we give a full description of such classes of groups.