Chen, Yan Signature of 4-manifolds with circle action. (Chinese. English summary) Zbl 1265.57012 J. Fudan Univ., Nat. Sci. 50, No. 1, 71-77, 86 (2011). Summary: It is proved that for a 4-dimensional connected closed \(S^1\)-manifold \(M\) with non-empty finite fixed point set, the equivariant cohomology ring \(H^*_G (M; \mathbb Q)\) of \(M\) with coefficients in \(\mathbb Q\), is a free \(H^* (BG; \mathbb Q)\) module. The main result is about the relationship between the signature \(\sigma (M)\) of \(M\) and the number of the fixed points \(|M^G|\). MSC: 57R91 Equivariant algebraic topology of manifolds 57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) 57S10 Compact groups of homeomorphisms Keywords:4-dimensional connected closed \(G\)-manifold; circle actions; equivariant cohomology rings; finite fixed point set; intersection form; signature PDFBibTeX XMLCite \textit{Y. Chen}, J. Fudan Univ., Nat. Sci. 50, No. 1, 71--77, 86 (2011; Zbl 1265.57012)