Actions of symplectic groups on certain manifolds
This paper studies smooth nontrivial actions of Sp(n), \(n\geq 7\), on a closed manifold X having the cohomology ring of a product \(P_ a({\mathbb{C}})\times P_ b({\mathbb{C}})\) or \(P_ a({\mathbb{H}})\times P_ b({\mathbb{C}})\) of complex or quaternionic projective spaces. A typical result says that if \(X\sim P_ a({\mathbb{C}})\times P_ b({\mathbb{C}})\) with 1\(\leq b\leq 4\leq 2n\) and \(a+b\leq 4n-3\), then \(a=2n-1\) and \(X=P_{2n- 1}({\mathbb{C}})\times Y\) where Sp(n) acts in the usual way on \(P_{2n- 1}({\mathbb{C}})\) and trivially on Y, with Y having the cohomology ring structure of \(P_ b({\mathbb{C}})\).
smooth actions of the symplectic group on a closed manifold having the cohomology ring of a product of complex or quaternionic projective spaces
scientific article; zbMATH DE number 3862067