The positive fundamental group of Sp(2) and Sp(4) (Q5925882)

This paper proves that the positive fundamental group of the symplectic group \(\text{Sp}(2n)\) injects into the ordinary fundamental group if \(n\leq 2\). Here a path \(A(t)\) is positive if the derivative satisfies \(A'(t)= JP_tA(t)\), where \(P_t\) is a positive definite symmetric matrix and \(J\) is the standard complex structure.