The Positive Fundamental Group of Sp(2) and Sp(4)

TL;DR

This paper investigates the homotopy classes of positive loops in the symplectic groups Sp(2) and Sp(4), establishing conditions under which positive loops are homotopic.

Contribution

It provides a characterization of positive loop homotopies in Sp(2) and Sp(4), clarifying their homotopy equivalence relations.

Findings

Positive loops in Sp(2) and Sp(4) are homotopic iff they are homotopic through positive loops.

The paper establishes a criterion for homotopy equivalence of positive loops in these groups.

Homotopy classes of positive loops are fully described in the studied groups.

Abstract

In this paper, we examine the homotopy classes of positive loops in Sp(2) and Sp(4). We show that two positive loops are homotopic if and only if they are homotopic through positive loops.