Group actions on 𝐴_{𝑘}-manifolds

Source abstract

By an A k {A_k} -manifold we mean a connected manifold with elements w i ∈ H 1 ( M ) , 1 ⩽ i ⩽ k {w_i} \in {H^1}(M),\,1 \leqslant i \leqslant k , such that w 1 ∪ ⋯ ∪ w k ≠ 0 {w_1} \cup \, \cdots \cup \,{w_k} \ne 0 . In this paper we study the fixed point set, degree of symmetry, semisimple degree of symmetry and gaps of transformation groups on A k {A_k} -manifolds.